Contradiction with 2 Samuel 6:9
This verse shows David fearing bringing the Ark to him, unlike the eagerness of the men of Kirjathjearim.
2 Samuel 6:9: And David was afraid of the LORD that day, and said, How shall the ark of the LORD come to me?
Contradiction with 1 Samuel 7:1
This verse indicates the Ark was taken to the house of Abinadab instead of being sought by another city as 1 Samuel 6:21 might imply.
1 Samuel 7:1: And the men of Kirjathjearim came, and fetched up the ark of the LORD, and brought it into the house of Abinadab in the hill, and sanctified Eleazar his son to keep the ark of the LORD.
Contradiction with 2 Samuel 6:2-3
David proactively seeks the Ark and transports it instead of waiting for it to be delivered as in 1 Samuel 6:21.
2 Samuel 6:2-3: And David arose, and went with all the people that [were] with him from Baale of Judah, to bring up from thence the ark of God, whose name is called by the name of the LORD of hosts that dwelleth [between] the cherubims. [Baale: or, Baalah, that is, Kirjathjearim] [whose name...: or, at which the name, even the name of the LORD of hosts, was called upon]
Contradiction with Numbers 4:15
This details specific instructions for moving the Ark, contrasting the lack of detail and proper procedure in 1 Samuel 6:21.
Numbers 4:15: And when Aaron and his sons have made an end of covering the sanctuary, and all the vessels of the sanctuary, as the camp is to set forward; after that, the sons of Kohath shall come to bear [it]: but they shall not touch [any] holy thing, lest they die. These [things are] the burden of the sons of Kohath in the tabernacle of the congregation.
Contradiction with 1 Chronicles 13:3
The people make a consensus to bring back the Ark, unlike the immediate and unilateral action suggested by 1 Samuel 6:21.
1 Chronicles 13:3: And let us bring again the ark of our God to us: for we enquired not at it in the days of Saul. [bring...: Heb. bring about]