What happens if you put on a police costume and go policing?

Intentionally deceovit about your identity, in order to obtain access to a something of value that you are forbidden to access, is a clear crime, as it should be.

Being deceptive about your identity during the commission of a crime is illegal?

If I dress up as a Best Buy employee and drag a television out of a loading dock and into the bed of a truck, that's definitely illegal, but I don't think it's any more illegal than if I did it in jeans and a T-shirt.

Impersonating a police officer is its own charge though, so while impersonating a best buy employee isn't going to get an extra charge applied, impersonating a cop, is.