Revealing mistake: When Rocky first stands up in the tank still bandaged, he doesn't get up directly underneath the colour machine, which he is going to grab onto moments later, because he can't see; you can see him trying to shuffle discreetly into the right position.
Continuity mistake: At the beginning of Columbia's solo in "The Time Warp" she is sitting on the jukebox and wearing her gold glitter hat. Then, during the refrain, we see the hat on the floor near the jukebox, sans Columbia. Immediately after the refrain, Columbia has her hat back on as she does her tap dance. [There's about 9 seconds that Columbia's off-screen that she could have retrieved it, and about 4 seconds Magenta and Riff Raff are off-screen and end up next to Columbia and could have picked it up and given it to her, but there's no reason for it to have been out in the middle of the floor to begin with.] (00:22:10)
Continuity mistake: In the scene where Brad and Janet first talk with Frank in the lab (before Frank's speech beginning with 'Tonight, my unconventional conventionalists...'), Frank makes a comment about how Brad is "so dominant." At that moment, Brad closes his robe but does not button it. However, when the camera switches angles, it is buttoned. (00:31:33)
Revealing mistake: After Frank-N-Furter pulls the lever to immobilize Janet, Brad and Dr. Scott, Janet's feet are positioned close together when Frank-N-Furter shouts, "Planet Schmanet Janet,", but when she screams, "Stop!" her supposedly immovable feet now have a space of about 2 ft. between them. (01:10:50)Super Grover
Continuity mistake: At the beginning when Brad and Janet get the flat tyre and it's raining, Brad says "Didn't we pass a castle back down the road a few miles?" before they get out of the car to go to the castle. If the castle was a few miles back, both of them should be soaking wet, and the paper Janet put over her head should have been soaked not long after they got out of the car. After they enter the driveway of the castle they get increasingly wet, but they are barely damp before this despite walking some distance in the constant rain. (00:13:25 - 00:14:25)
Revealing mistake: In the laboratory, when the tank is unveiled, fishing lines are visible strung across the top of the tank (probably to keep the red sheet from dipping down into the water). Watch closely in the reverse shot after Magenta and Columbia throw off the sheet. (00:33:45)
Continuity mistake: As Magenta is undressing Brad she throws Columbia his pullover - twice. (00:28:20)