If I were invisible the first thing I would do wouldn't be enter an area filled with naked members of the opposite sex.
I would pretend to be a ghost in a bank and figure out how to disable all of the cameras (so they wouldn't see the money floating away later on.) Then I would figure out how to open the safe, THEN figure out how to disable the alarms so the police don't show up quick enough to shoot blindly and hit me. After that I would scare everyone into leaving the bank and rob the place. To escape home I would scare someone into giving me their car. I wouldn't want to be invisible forever, I'm sure that would be a pain in the ass. Everyone would be stepping on my toes all the time and bumping into me. Of course, when pretending to be a ghost I would need to leave the water running in houses, because apparently that's what ghosts like to do.
This plan would only work if everyone is afraid of disembodied voices.