Continuity mistake: When we first see Marty on the floor oiling his chair, his cane is lying on the floor with the handle end pointing towards the kitchen. When he picks it up a few shots later, it has turned 180 degrees and the handle is pointing towards the door. At no time did he touch it.
Continuity mistake: After Rick has left Roz's apartment, she goes into the kitchen with the roses and just as she gets there Frasier knocks on the door. Within a couple of seconds she comes back with the roses in a vase, but she just didn't have enough time to do this in "real time".
Continuity mistake: Abbie puts Niles' burning menu in the ice bucket where it remains for the rest of the scene, next to the bottle of champagne. Sometimes the menu is right up against the bottle and sometimes it is an inch or two apart - with no one touching either item.
Continuity mistake: Abby orders Frasier out of her office and she bends down to pick up his jacket from the floor, even though it had been on the chair throughout the scene. She then throws it and his overcoat out the door after him - we see the jacket land on the floor and the overcoat on his head. She slams the door and the shot goes to Frasier - the jacket is now draping his head, rather than the overcoat.
Continuity mistake: Near the end of the show, Niles and Frasier are shaping hamburger patties in the kitchen. Niles has a blue bottle of water which sits on the stove top in front of him. In one shot it suddenly appears on the counter to his right; even though Niles hadn't moved it. By the end of the scene it is back in front of him on the stove top.
Continuity mistake: In the last scene of this part of the show, where Frasier is trying to figure out if Cassandra is romantically interested in him - he removes his outer clothes and stands in front of her closet. We see his clothes change position several times. Sometimes they are on the back of the chair, sometimes they are on the floor. His shoes also change places. In fact, the shoes appear to move on their own at one point and are pulled tidily to one side.