Contradiction with Numbers 16:40
This verse emphasizes that only Aaron's descendants should offer incense, while 2 Chronicles 26:17 shows non-Aaronic Levites with abilities to do sacred duties.
Numbers 16:40: [To be] a memorial unto the children of Israel, that no stranger, which [is] not of the seed of Aaron, come near to offer incense before the LORD; that he be not as Korah, and as his company: as the LORD said to him by the hand of Moses.
Contradiction with Numbers 18:7
This verse designates the responsibility of the altar exclusively to Aaron and his sons, yet 2 Chronicles 26:17 implies support from non-Aaronic priests is acceptable.
Numbers 18:7: Therefore thou and thy sons with thee shall keep your priest's office for every thing of the altar, and within the vail; and ye shall serve: I have given your priest's office [unto you] as a service of gift: and the stranger that cometh nigh shall be put to death.
Contradiction with 2 Samuel 6:6-7
Uzzah is punished for touching the ark, enforcing strictness on sacred duties, whereas 2 Chronicles 26:17 seems to allow some leniency with Uzziah and other roles.
2 Samuel 6:6-7: And when they came to Nachon's threshingfloor, Uzzah put forth [his hand] to the ark of God, and took hold of it; for the oxen shook [it]. [Nachon: also called Chidon] [shook it: or, stumbled]