(at around 27 mins) When Dr. Hendrickson asks Wayne Szalinski what language Adam was speaking he responds Yugoslavian. There is no such language as Yugoslavian. The official languages of Yugoslavia, before it broke up into separate countries, are Serbo-Croatian, Slovenian, and Macedonian.
(at around 54 mins) When Clifford asks Wayne what could be causing Adam to grow, Wayne says "Yesterday, when I gave him lunch, he was right near the microwave oven", when, in fact, that happened earlier that same day.
(at around 10 mins) Early in the film Dr. Henderson storms out of the lab and walks past a portrait of Clifford Stirling. In the following camera shots, he is directly in front of the portrait then beyond it again.
In one scene when Adam is on Fremont St. in downtown Las Vegas the marquee for Circus Circus is behind him. However, all the other signs are for casinos on Fremont St. The Circus Circus sign is not shown again.
(at around 29 mins) Wayne tells Nick about the reason why he made them all promise to never tell anyone that him and his sister (which would have included the neighbors children) were once shrunk and lost to them (which happened in the original.) When Wayne brings that up to Nick, he claims that they were "shrunk and lost for two days", when in fact, that only happened for one day.
The final scene--and the punchline--of the first film features the shrinking machine in reverse, and the family feasts on enlarged food. In fact, reversing the effects of the machine is how the kids went from tiny to normal size. In the second film, Wayne is working for a company that is testing a completely different machine that will enlarge things, and the shrink machine is in storage. It is never explained why simply reversing his shrink machine wasn't the answer.