During the Passover scene, Moses and his family are starting to have dinner and Moses' Egyptian mother comes to the house to seeking a place to stay. As all of this is going on the old man at the table keeps reciting the Psalms. This would be difficult to do since King David wrote the Psalms and he didn't come into the picture until the book of Kings.
David did indeed record most of the Psalms we have in the Bible (some are thought to be written by his son Solomon) but the Jewish people already had psalms when Moses was around. Psalms are just a catchall term for prayers and hymns of praise. It's quite possible that many of those David recorded were traditional psalms, passed down. He wasn't necessarily the original author of all of the psalms he recorded. Could be a slipup, might not be. Artistic license, I suppose.
Not all the psalms were written by David. Read Psalms 90 and 91, and many Bibles identify these as written by Moses. Besides, David was not the only writer of Psalms. Moses, Gat, Solomon, and others wrote them.