I don't think very many people consider the process by which the Bible came about to be something infallible (and if they do, I would wonder how much they know about it). Christians aren't like the Muslims or the Mormons who claim they have the exact word of God that came down from heaven via an angel or golden tablets, or whatever. Humans wrote books inspired by God, though we have to figure out which of those books were inspired by God.
I have recently begun reading the apocrypha with the intent of seeing if perhaps any of these books belong in the cannon (it has been quite interesting). I've only read Tobit, Judith, the additions to Esther, and bits of the Wisdom of Solomon thus far. In the case of Tobit and Judith, I feel that they are almost certainly fiction stories.
Tobit begins in the first person, then shifts abruptly to the third person. There isn't anything really wrong about this, except it is quite awkward to me because Tobit is busy describing in very minute detail his righteousness (imagine Job describing how he acted, with a very proud voice- this is how Tobit opens, and I couldn't help but be reminded of the man who prayed "God, thank you that I am not like the sinners"). When reading this I was trying to think of reasons why it could possibly be written like this, and the only reason plausible explanation was "for entertainment value." I suppose perhaps there may be better reasons than this, but I couldn't figure any out. In Sarah, the woman who eventually marries Tobit's son Tobias, there is supposedly a demon who killed her first seven husbands the day of their marriage. I do not think God would allow a demon to have this much power over a person- compare this to Job, where even Satan is not allowed to strike Job down. At some point Tobit is blinded, and an angel basically tells Tobias how to drive out the demon and cure the blindness with parts of a fish. This seemed almost magical/alchemical in nature- the implication in the text it was the fish parts that accomplished the healing/exorcism, whereas in most other miracles the means by which the miracle are accomplished have very little to do with the healing except the person had faith in it. To me, this story feels like the author began with Job as the basic story outline, and then just added whatever he felt like to make a good story. Of course, one could argue whether Job is a parable or actually happened, but either way Job has a lot of utility as scripture. I don't think the same is particularly true of Tobit (feel free to disagree).
Judith has several major inconsistencies which lead me to believe that it was written by a very inattentive author attempting to make a good story. The city of Bethulia is under siege, and they run out of water rations. Judith manages to convince the leaders to let her (and one of her servants) out of the city so she might let God work through her and turn back the enemy. The first thing she does (after praying to God to let her deceit bring down the enemy) is go take a bath. While everyone else has been fainting from lack of water. Something is seriously amiss here. Either the author just glossed over this fact when writing the story, or Judith was letting everyone else practically die to make herself look pretty. She also seems to have a fair bit of wine stashed away too, so it wasn't just water either. She's a widow who essentially dresses up as finely as she can to parade in front of foreign men- while she lies to them so "God can have a great victory." To me, this all points toward fiction- this story sounds an awful lot like Jael's story, only with a lot of embellishment. I can't think of any other great victories God won through someone lying (Jacob got Esau's blessing through deceit, Abraham was deceitful about his wife, but God blessed these people in spite of their lack of faith, not because of).
As far as the additions to Esther go, they were added in the Greek and weren't in the original Hebrew. There isn't really much to say here, other than the Greek contradicts the Hebrew at times, and it almost certainly shouldn't be there.
Wisdom of Solomon was probably not written by Solomon, although this in itself isn't reason to discard it. I haven't really read much of it yet (the first few chapters), but I will say that I don't really read the "prophecy" in the second chapter as being about Jesus specifically. Taken by itself, verses 12-24 seem to refer to Jesus, but I take verse 10 to indicate that this is in reference to a generic righteous man and not to Jesus specifically (especially if you continue reading into chapter 3- "But the souls of the righteous are in the hand of God"). Compare it to Isaiah where there are very specific things that are mentioned. One could argue that chapter 2 of Wisdom of Solomon applied to most prophets that died at the hands of the Israelites, with the exception of calling themselves "child of the Lord." That's my position at the moment, though that might change as I read more of the book.
As far as why any of these books were ever in the Bible to begin with, I think the typical Christian belief is that the Old Testament commandments are still valid where the New reaffirms it. You won't find quotation from any of the apocryphal books in the New Testament, although the writing may echo some of them (Romans and Wisdom, 2 Corinthians and Wisdom, James and Sirach). As such, any damage that having these books in the Bible could cause are somewhat minimal. I would be far more worried about the cannon of the New Testament.