It is often proposed that the material in Chronicles "contradicts" the similar material found in the books of Samuel and Kings. This is usually based on the observation that Chronicles tells us many things about the kings of Judah that are not told to us by the Books of Kings. That, of course, does not constitute a contradiction, merely a difference. Most of the differences between Chronicles and Kings can be explained by a consideration of the intent of the writer of Chronicles insofar as he makes it plain to us. It is clear, for example, that Chronicles is concerned primarily with the Davidic dynasty and the Solomonic temple, the latter attended by the Aaronic priesthood and the Levites. Note, as something of a programmatic text for that theme, 2 Chron 13:1-12.
In brief, the statement can be accurately made that the Books of Kings probably reached their final form during the period of the exile, and were written to demonstrate to the people that the destruction of Jerusalem and the exile itself were the just judgment of God upon a long disobedient people. The Books of Chronicles were written in the postexilic period with a view to encouraging the people that all hope was not lost, and that God was still merciful and gracious.
It is also apparent that the author of Chronicles knew the books of Samuel and Kings, since he drew a great deal of material from them, either verbatim or almost verbatim. Thus, it seems likely that he also supposed that his readers would have known those works, or at least to some extent have been familiar with them. Thus, material in Samuel-Kings, not suitable to the purpose of the author of Chronicles, has simply been omitted, the author knowing his readers would have been aware of the material in his sources. This explains the omission of David's committing of adultery and murder in the affair of Bathsheba. That episode was not pertinent to the author's purpose, and was thus omitted. Likewise, the repentance of Manasseh, found in Chronicles but not in Kings, suits the purposes of the former, but not the latter. The two accounts together give us a fuller view of the events of the period of the Israelite monarchy.
The most substantive discrepancies between the two accounts have to do with the numbers reported on various occasions. For example, compare 2 Sam 24:9 with 1 Chron 21:5. Both accounts treat of David's census. The first says, "in Israel there were 800,000 valiant men who drew the sword, and the men of Judah were 500,000." The second passage says, "In all Israel there were 1,100,000 men who drew the sword, and in Judah 470,000 who drew the sword." There are two possible ways of dealing with this discrepancy. The first is to take the view that we are dealing with textual difficulties in the source or sources used by the authors. That is certainly a plausible explanation. The second approach is to consider that the numbers have references to somewhat different groups of people. So with Israel, the 800,000 would be those who were "valiant men," whereas the 1,100,000 would be the total. For Judah, the 470,000 would be those who "drew the sword," whereas the 500,000 would be the total.
In short, most of the difficulties are more apparent than real. For intersted readers, I would recommend Haley's
Alleged Discrepancies of the Bible and Gleason Archer's
Encyclopedia of Bible Difficulties.