In the scene where Mitch and Hannah walk along the Vegas strip, passers-by can be seen trying to interact with Mitch. Per Gugu Mbatha-Raw, this was 100 percent unscripted. The Strip had not been blocked off prior to shooting, so people eagerly seized the opportunity for a little face time with Steve Carell. Since MITCH happens to be extremely famous (and well-liked, at least at that point) in-universe, Carell just went with it.
When Martin Short does his dance number you can see him do his signature "Ed Grimley" stance from when he played that character, putting his legs together and comically bending his knees.
The views of the strip depict the Park hotel, but at time of shooting it was the Monte Carlo .