Continuity mistake: At the beginning of the show, Frasier is sitting with Martin and Niles in Cafe Nervosa telling them about the radio play. As Marty says "we were a simple people", Frasier manages to open his briefcase, take out the script, put it on the table, and put his briefcase back on the floor and be sitting still - all in about 3 seconds. This just wouldn't be possible in real time.
Continuity mistake: When Martin and Shelly are having a fight, Frasier puts a small bag down, which is yellow on one side and has a logo on the other. He puts it down with the yellow side facing us, and for a several shots it stays like that. However, when Martin is talking about "things that bugged me," you see the bag has inexplicably rotated so the logo is now facing us.David Mercier
Continuity mistake: Frasier and Roz are in Cafe Nervosa and Roz is looking at a newspaper while Frasier talks about giving Donny a bachelor party. Roz puts the paper in her lap, but in the next shot over her shoulder we can see that she is still holding the paper up.
Continuity mistake: Frasier's third date, Leslie, shows up at his apartment wearing a long off-white coat. He hangs it up beside the fireplace; for the rest of the scene we sometimes see the coat hanging with the left sleeve straight and sometimes with the left sleeve all crinkled up.
Continuity mistake: Maris is hiding in a wooden box so she will be shipped out of the country. Marta, her housekeeper, has a protein shake for her, and puts the straw through a hole in the box. Maris indicates that she's drunk too much and Marta goes to put the straw back in the hole so she can regurgitate some - but just before that happens we see a stream of the liquid come out of the hole and dribble down the box. In the next shot the straw goes into the hole and the box is all clean and dry again.