When Martin and his partner are driving, the weather is grey and rainy, but when he pulls in to the diner parking lot it is instantly sunny and dry. This is a bit too immediate, even for Seattle's temperamental weather.
Right after Frasier suggests that Mrs. Kurtzman could walk Eddie, a four-plug floor outlet is visible in front of the television.
About 14 minutes into the episode, Martin (John Mahoney) is putting the final touches on his uniform in the mirror. The scene apparently required John Mahoney to finish up and then think back to the day he was shot. Clearly, however, he can't get the name tag attached to his pocket in time, so just holds it on with his finger as the scene dissolves to the flashback.