Stupidity: When Riker and Worf are searching for Geordi on the holodeck, why don't they just terminate the program, instead of looking for him in the simulated jungle? Would have made it a heck of a lot easier to find him in the relatively small empty holodeck, invisible or not.
Stupidity: Picard has to stop Worf from blasting a hole into the front visor of the bridge when Q appears in it. Even back in the XX century nobody would try to shoot at the TV screen because something appears in it (our TVs being also placed generally in less important positions)! And someone with this degree of imbecility is the high ranking security officer, even.
Stupidity: Why would the miners send a shuttle to get Captain Picard when the Enterprise has a compliment of shuttlecraft on board? Also, how could the Enterprise engineering team (led by Lt. Commander LaForge) miss that the thruster quad on the shuttle was near failure?