A deep undercover FBI agent wouldn't be carrying his ID around with him while he's on the case with his suspects.
After Ritter takes the gag off Whirtle and is threatening him for the safe combination, a shadow of the boom microphone can be seen moving on the wall behind Ritter.
When the water gets turned off while Jerry is in the shower, his hair, face and upper body are covered in soap. But in the long shot of him peering out of the shower, there's hardly any soap to be seen. The next shot of him back in the shower, all the soap lather reappears.