Bulldog could not have had Frasier's car towed away from his spot at work and replaced with a wrecked version to prank him when Frasier showed up for work at the beginning of his shift, since Frasier drove to work. The whole beginning scene therefor doesn't make any sense. If Frasier had happened to be leaving work at the end of his shift and found the wrecked car there, that would have given Bulldog the time to switch out the cars. Somebody wasn't thinking when they wrote this.
In the sheet of paper that Gertrude gives the courier man, which is supposed to contain the address of the school, there's no address. It just has the text that he is supposed to say to the boy.
Mrs Moon holds onto piece of bicycle she removed. It is impossible to remove crankshaft and pedals all in one piece, What she was holding was four separate parts that have to be removed separate but not in one piece as shown.