At the conclusion of the flashback of Monk in eighth grade, the principal of Monk's school flashes a Series 1999-2003 $5 Note. Since this note was not first issued until May 2000 and the flashback is dated April 12, 1972, such a note would have been unavailable.
When young Monk is being detained by the bullies in the Boys Restroom, it appears the urinals have automatic flush mechanisms installed. The scene takes place in the 1970s when no such mechanisms existed.
In the junior high flashback scene where Leo takes young Monk's clarinet, the picture in Monk's locker disappears as he talks about the stolen money - and reappears in the next shot when Leo takes the clarinet.