I remember reading about how the essenes, a jewish sect of the time, had a different calender which would make the date of the passover occur on a different date. Thus it could have been celebrated on different days by different Jews in the same year. I don't know if any Jews would have celebrated it twice, somehow, just to be on the safe side?
Myself, when I did look into this, and I don't remember all the points of it, I think I sided with John's and somehow interpreted the synoptics to agree with it. But unfortuanatly, I don't remember the details. But probably it is better to side with the synoptics, as a lot of John's gospel is considered to have been written later then the synoptics.
Here's the relavent info on the days if anyone cared to try and figure it out.
Postexilic Observance. After the return of the Jews from captivity the celebration of the Passover, like that of other institutions, became more regular and systematic; and its laws, rites, manners, and customs have been faithfully transmitted to us. These were the same as those in the time of Christ and His apostles and are, therefore, of the utmost importance and interest to us in understanding the NT. We give the various practices in connection with the days of the festival on which they were respectively observed.
1. The Great Sabbath (10th Nisan). The Sabbath immediately preceding the Passover, it is so called because, according to tradition, the 10th of Nisan, when the paschal lamb was to be selected, originally fell on the Sabbath. In later legislation the animal was not required to be set aside four days beforehand, yet the Sabbath was used for the instruction of the people in the duties of this great festival. In addition to the regular ritual, special prayers bearing on the redemption from Egypt, the love of God to Israel, and Israel's obligation to keep the Passover, were prescribed for that Sabbath. <Malachi 3:1-4:6> was read as the lesson of the day, and discourses were delivered explaining the laws and domestic duties connected with the festival. This is likely the Sabbath referred to in <John 19:31>.
2. The 13th Nisan. On the evening of the 13th Nisan, which, until that of the 14th, was called the "preparation for the Passover" <John 19:14>, every head of a family searched for and collected by the light of a candle all the leaven. Before beginning the search, he pronounced the following benediction: "Blessed art thou, O Lord our God, King of the universe, who has sanctified us with thy commandments, and hast enjoined us to remove the leaven." After the search he said, "Whatever leaven remains in my possession which I cannot see, behold, it is null, and accounted as the dust of the earth."
3. The 14th Nisan. This day, called until the evening the preparation for the Passover, was also known as the "first day" of Passover <Lev. 23:5-7>. Handicraftsmen, with the exception of tailors, barbers, and laundresses, were obliged to cease from work, either from morning or from noon, according to the custom of the different places in Palestine. No leaven was allowed to be eaten after noon, when all that had been found either on this day or the preceding one was to be burned. On the 14th Nisan every Israelite who was physically able, not in a state of Levitical uncleanness, or further distant from Jerusalem than fifteen miles, was to appear before the Lord with an offering proportionate to his means <Exo. 23:15; Deut. 16:16-17>. Women, though not legally bound to appear in the sanctuary, were not excluded <1 Sam. 1:7; Luke 2:41-42>.
4. Offering of the Paschal Lamb. The lamb was to be free from all blemish and neither less than eight days nor more than exactly one year old. Each paschal lamb was to serve a "company" of not less than ten nor more than twenty, the representatives of each company going to the Temple. The daily evening sacrifice <Exo. 29:38-39>, usually killed at the eighth and a half hour (i.e., 2:30 P.M.), and offered up at the ninth and a half hour (i.e., 3:30 P.M.), was on this day killed at 1:30 and offered at 2:30 P.M., an hour earlier. And if the 14th of Nisan happened on a Friday, it was killed at <12:30> and offered at 1:30 P.M., two hours earlier than usual, so as to avoid any needless breach of the Sabbath.
Before the incense was burned or the lamps were trimmed, the paschal sacrifice had to be offered. It was done in this way: The first of the three festive divisions, with their paschal lambs, was admitted within the court of the priests. Each division was to consist of not less than thirty persons. Immediately, the massive gates were closed behind them, and the priests blew a threefold blast from their silver trumpets when the Passover was slain; altogether, the scene was most impressive. All along the court up to the altar of burnt offering priests stood in two rows, the one holding golden, the other silver, bowls. In these the blood of the paschal lambs, which each Israelite slew for himself (as representative of his company at the paschal supper), was caught up by a priest, who handed it to his colleague, receiving back an empty bowl, and so the bowls with the blood were passed up to the priest at the altar, who jerked it in one jet at the base of the altar. While this was going on, a most solemn "hymn" of praise was raised, the Levites leading in the song and the officers either repeating after them or merely responding. "The Hallel [which see] was recited the whole time, and if it was finished before all the paschal animals were slain it might be repeated a second and even a third time. Next the sacrifices were hung up on hooks along the court, or laid on staves which rested on the shoulders of two men (on Sabbaths they were not laid on staves), then flayed, the entrails taken out and cleansed, and the inside fat separated, put in a dish, salted, and placed on the fire of the altar of burnt offering. This completed the sacrifice.
"The first division of officers being dismissed, the second entered, and finally the third, the service in each case being conducted in precisely the same manner. Then the whole service concluded by burning the incense and trimming the lamps for the night." If it was the Sabbath, the first division waited in the court of the Gentiles, the second between the ramparts, i.e., the open space between the walls of the court of the women and the trellis work in the Temple, whereas the third remained in its place. At dark all went out to roast their paschal sacrifices. According to Jewish ordinance, the paschal lamb was roasted on a spit of pomegranate wood, the spit passing through from mouth to vent. If it touched the oven, the part so touched was to be cut away, thus carrying out the idea that the lamb must not be defiled by any contact with foreign matter. It was not to be "sodden," because the flesh must remain pure, without the addition even of water, and no bone of it was to be broken.
5. The Paschal Supper. As the guests gathered around the paschal table they were arrayed in their best festive garments, joyous and at rest, as became the children of a king. To express this idea the rabbis insisted that at least a part of the feast should be partaken in a recumbent position. The left elbow was placed on the table, the head resting on the hand, with sufficient room between each guest for the free movement of the right hand. This explains in what sense John "was reclining on Jesus' breast," and afterward "leaning back thus on Jesus' breast," when he leaned back to speak to Him <John 13:23,25; Luke 22:14>. The father, or other person presiding, took the place of honor at the table, probably somewhat raised above the rest.
The paschal supper commenced by the head of the "company" pronouncing a benediction over the first cup of wine, which had been filled for each person. It was then drunk, and a basin of water and a towel were handed around or the guests got up to wash their hands <John 13:4-5,12>, after which the appropriate blessing was pronounced.
These preliminaries ended, a table was brought in, upon which was the paschal meal. The president of the feast first took some of the herbs, dipped them in the sauce (Heb. charoseth), ate some, and gave to the others <Matt. 26:23; John 13:26>. Immediately after this all the dishes were removed from the table (to excite curiosity), and the second cup of wine was filled. Then the son asked his father as follows: "Wherefore is this night distinguished from all other nights? For on all other nights we eat leavened or unleavened bread, but on this night only unleavened bread? On all other nights we eat any kind of herbs, but on this night only bitter herbs? On all other nights we eat meat roasted, stewed, or boiled but on this night only roasted? On all other nights we dip [the herbs] only once, but on this night twice?" In reply the head of the house related the whole national history, commencing with Terah, Abraham's father, Israel's deliverance from Egypt, and the giving of the law.
The paschal dishes were now placed back upon the table. The president took up in succession the dish with the Passover lamb, that with the bitter herbs, and that with the unleavened bread, briefly explaining the importance of each; the first part of the Hallel was sung <Pss. 113 and 114>, with this brief thanksgiving at the close: "Blessed art thou, Jehovah our God, King of the universe, who hast redeemed us and redeemed our fathers from Egypt." The second cup of wine was then drunk, and hands were washed a second time, with the same prayer as before, and one of the two unleavened cakes broken and "thanks given."
Pieces of the broken cake, with "bitter herbs" between them and "dipped" in the charoseth, were next handed to each of the company. This, in all probability, was the "dipped morsel" which, in answer to John's inquiry about the betrayer, the Lord "gave" to Judas <John 13:25-30; cf. Mark 14:22; Luke 22:21>.
The paschal supper itself consisted of the unleavened bread, with bitter herbs, of the so-called Chagigah (i.e., a voluntary peace offering made by private individuals), and the paschal lamb itself. After that nothing more was to be eaten, so that the flesh of the paschal sacrifice might be the last meat partaken of. But since the cessation of the paschal sacrifice, the Jews conclude the supper with a piece of unleavened cake called the Aphikomen, or after dish. Hands were again washed, the third cup was filled, and grace after meat said. The service concluded with the fourth cups over which the second portion of the Hallel was sung <Pss. 115-18>, the whole ending with the so-called "blessing of the song."
6. The 15th Nisan, Unleavened Bread. On this day there was a holy convocation, and it was one of the six days on which, as on the Sabbath, no manner of work was allowed, with this exception: whereas on the Sabbath the preparation of necessary food was not allowed <Exo. 16:5,23,29; 35:2-3>, on holy convocation it was permitted <12:16; Lev. 23:7; Num. 28:18>. The other five days on which the Bible prohibits servile work are the seventh of this festival, the day of Pentecost, New Year's Day, and the first and last of the feast of Booths (Tabernacles, KJV).
In addition to the ordinary sacrifices there were offered on this and the following six days two bulls, a ram, and seven lambs of the first year (with grain offerings) for a burnt offering, and a goat for a sin offering (28:19-23). Besides these public sacrifices voluntary offerings were made by each individual appearing before the Lord in Jerusalem <Exo. 23:15; Deut. 16:16>. The Jewish canon prescribed that this freewill offering should be a burnt offering, worth not less than sixteen grains of corn; a festive offering of not less value than thirty-two grains; and a peace, or joyful offering <27:7>, the value to be determined by the offerer <16:16-17>.
from New Unger's Bible Dictionary)
(originally published by Moody Press of Chicago, Illinois. Copyright (C) 1988.)