In essence, I'm asking about whether there are any historical inaccuracies in the movies/plays themselves. I'm pretty sure the book would have very few, due to the fact that it was written in a similar time, but what about in the movies/plays?
The points that Samuel raised are all valid, books don't really attempt to present a fair and balanced depiction of events, however I still think it's a good question, and to answer your question directly:
Yes, for the most part it is pretty accurate, as long as you recognize the perspective that it's coming from. As the title suggests, the book is focused on the lowest rungs of society, so the feelings of desperation and oppression come as much from the social class as they do from the time period. Not everyone in France was that desperate or oppressed.
The uprising portrayed is the June Rebellion of 1830 and for the most part that is depicted accurately. It began after the funeral of Lamarque, and it was a mixture of the poorest people of Paris (who were almost always ready to rebel), and wealthier intellectuals from secret societies who fought for a variety of idealist causes. It never caught on and was quickly crushed by the military with moderate casualties on both sides.
As for the characters, Valjean and Javert are both pretty exaggerated (to be expected), but none of the beliefs expressed in the book would be uncommon or unlikely at the time. As far as accuracy goes, it's probably one of the most historically valid fictional works out there. It's an honest depiction of a series of events as seen and experienced by one segment of society. Granted, the harmonies in the musical version are probably much tighter than they were at the time.
Novels are not typically accorded a high status as a primary source by historians because they have a purpose other than the truthful representation of the past as it was, as recreated from the documentary records of the past. Novels are incapable of "accuracy" in this sense. Similarly: plays and movies are incapable of historical accuracy.
Novels may present a useful way for readers to encounter the sentiment of the past, or the sentiment of a novellist regarding the past. They may provide a complex and difficult to interpret primary source, or a jumping off point.
They're not the place to go for the social or cultural history of France in the early 19th century.