In part 1, the gang met the Professor when Perozzi's kid was grownup, while in the flashback in part 2, the Professor is already hanging out with gang, when Perozzi's kid is still a kid.
Or am I wrong?
Besides that, both films very entertaining.
Yes, the kid seems to be problematic to continuity. From the goofs:
Count Mascetti hosts Perozzi's son as a grammar school kid in the very same house where he lives in My Friends, but in the former movie we see how the house is first rented by Mascetti when Perozzi's son is a fully grownup adult.
Happiness is a belt-fed weapon.