It's never explain how Kelly got into the Attic when she's obviously under 18 like her friends, unless Screech made her a fake ID too.
Screech makes fake photo IDs for the gang. However, he develops the photos in a brightly lit classroom instead of a darkroom. The pictures would not have developed properly.
Mr. Belding (who is the school Principal) is inexplicably teaching the Photography class. There should be a substitute teacher (or the regular teacher) teaching the class and not the Principal who presumably has other things he should be doing.
The Gang seems intent on not letting Kelly see that Jeff is cheating on her at the club, but the entire reason they went back to the club is to take a picture of Jeff cheating to show Kelly, so they should actually want her to see him cheating.
The bouncer at the Attic claims that he can spot a fake ID a mile away, but he's easily convinced by Zack's, Slater's and Screech's fake IDs.