Encounter at Farpoint (2) - S1-E2
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.