When Alex gets home from getting her friend out of the strip club her and nick get into a fight and when she starts slapping his face she hits the window blind causing it to roll up but in the next scene it is down again.
After she rescues Jeanie from the strip club, Alex rides her bicycle home in the pouring rain where Nick is waiting. Nick's hair is wet, but Alex' hair appears impossibly dry (outside and inside the apartment).
When Alex is dancing in the red suit and white face makeup, she just has the red suit on. When we see her again moments later, she has blue leggings on underneath the skirt, which weren't there before.
During the first dance number ("He's a Dream"), there is a three-second cutaway to the audience, and when we return to Alex, the pull chain for the water-dump has appeared from nowhere. Later in the dance, another shot from a similar angle shows that it has disappeared again. We know that Mawby's Bar didn't go to the unlikely trouble of elevating the chain out of sight except for the time when it was needed, because if they had, the sudden movement would set it swinging, and we don't see that.
In the restaurant scene where Alex is eating lobster, her nails are painted red. In the following scene (later that night) where she is playing with Nick's watch in bed, her nails are unpainted.
After finding out Nick helped her get the audition for the Pittsburgh Conservatory of Dance and storms out on him, she spends the next week moping at her place with the phone off the hook. When she finally decides to call Mawby's to talk to Jeannie, the hang-up beeps are still heard. Those stop beeping after about a minute or so initially, and wouldn't be beeping all through the week as it seemed.
In the climactic dance, Alex is played by several noticeably different people.
During the strobe light dance sequence at the end of song, the camera moves in close. The shadow of the camera person can clearly be seen on the right side of the screen.
Alex is shown using only a plastic face shield while operating an angle grinder. OSHA requires eye protection also (goggles) whenever face protection is needed.