Contradiction with Genesis 41:14
Joseph was brought hastily out of the dungeon to interpret Pharaoh's dream, similar to Daniel being brought before the king, but Joseph was exalted more immediately.
Genesis 41:14: Then Pharaoh sent and called Joseph, and they brought him hastily out of the dungeon: and he shaved [himself], and changed his raiment, and came in unto Pharaoh. [brought...: Heb. made him run]
Contradiction with Daniel 1:6
Daniel had already been introduced and was serving in the king's court prior to Daniel 5, but Daniel 5:13 implies a reintroduction.
Daniel 1:6: Now among these were of the children of Judah, Daniel, Hananiah, Mishael, and Azariah:
Contradiction with Daniel 2:48
Daniel was made a high-ranking official in the kingdom earlier, which contradicts the notion of him being unknown to the new king in Daniel 5:13.
Daniel 2:48: Then the king made Daniel a great man, and gave him many great gifts, and made him ruler over the whole province of Babylon, and chief of the governors over all the wise [men] of Babylon.
Contradiction with Daniel 4:8-9
The previous king, Nebuchadnezzar, knew Daniel well and had acknowledged his abilities to interpret dreams, unlike Belshazzar's apparent unfamiliarity.
Daniel 4:8-9: But at the last Daniel came in before me, whose name [was] Belteshazzar, according to the name of my god, and in whom [is] the spirit of the holy gods: and before him I told the dream, [saying],