Continuity mistake: The gang is reading through the script and Roz cues Bulldog and as she does we can see Gil has his script opened up on his knee. As the shot goes to Bulldog, Gil's script is now folded over and his pencil is in his right hand. He wouldn't have had time to change position.
Continuity mistake: The gang from the radio station is at Frasier's rehearsing for the radio play - Gil is sitting to the right of Marty's little table - he leans towards the table and puts his hand around a bottle of water but in the next shot he is pulling back from the table with a pencil in his hand, not the water. At the same time Bulldog, next to him, while Gil is reaching for his water, is holding his own water in front of him. When Gil pulls back with the pencil, Bulldog's arm is pulling his arm back from the left too.
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.