Reservoir Dogs
Reservoir Dogs was the film that put Quentin Tarantino on the map. Though the characters handcuffed policeman Marvin Nash behind his back, the next shot depicts Nash's hands cuffed together in the front. So much for continuity.
Grease
Right before the cast launches into the "Beauty School Dropout" number in Grease's soda shop scene, this waitress flips the light switch with her elbow as she juggles a tray of glassware. The only problem? She missed the switch by about a mile.