When Elwood Box arrives early to collect Max's body, he asserts that due to Max's (impending) death, his apartment is now government property. It is established throughout the series that Max rents his apartment from a private landlady, who does not know he is a spy, and whose ownership of the premises would be unaffected by the circumstances of a tenant's death.
When the Chief and 99 are trying to find Max in the Health Club, they go through a door marked Gymnasium however when the angle changes they are walking through the door marked Mr Hercules.
As Max and 99 are investigating the gym, he walks into a door leaving an obvious makeup stain. As the camera changes view while he walks through the door, the mark is gone.
In the health club, the doors leading from the hallway into the massage rooms and gymnasium have deadbolt locks on the outside (to lock patrons in), when they should be on the inside (to lock intruders out).
During the fight scene in the gym, Don Adams' stunt double can be clearly seen in several shots.