Contradiction with Exodus 12:33
Exodus 12:33 describes the Egyptians urging the Israelites to leave quickly because they were afraid of further plagues, while Psalms 105:38 suggests the Egyptians were glad when they departed.
Exodus 12:33: And the Egyptians were urgent upon the people, that they might send them out of the land in haste; for they said, We [be] all dead [men].
Contradiction with Exodus 12:31
In Exodus 12:31 Pharaoh calls Moses and Aaron to rise up and go with the Israelites, which implies urgency rather than gladness, contrasting with the tone implied in Psalms 105:38.
Exodus 12:31: And he called for Moses and Aaron by night, and said, Rise up, [and] get you forth from among my people, both ye and the children of Israel; and go, serve the LORD, as ye have said.
Contradiction with Exodus 14:5
Exodus 14:5 notes Pharaoh and his servants regretting the Israelites' departure, which contradicts the idea that the Egyptians were glad to see them leave in Psalms 105:38.
Exodus 14:5: And it was told the king of Egypt that the people fled: and the heart of Pharaoh and of his servants was turned against the people, and they said, Why have we done this, that we have let Israel go from serving us?
Contradiction with Exodus 10:28
In Exodus 10:28, Pharaoh tells Moses he doesn't want to see him again, showing anger and frustration, whereas Psalms 105:38 portrays Egyptians as glad.
Exodus 10:28: And Pharaoh said unto him, Get thee from me, take heed to thyself, see my face no more; for in [that] day thou seest my face thou shalt die.