for fun he should show the wife pictures of the puppy playing in the snow.
"Look at these cute pictures of my puppy!" etc. etc.
See if the wife notices the car or anything.
In reality though, it's hard to know what to do. I don't think it should be ignored, because even if she is 18, if she's a high school student where the coach works, she's off limits. End of story. However, if it's reported to the school, it stays on his employment record as a report whether he's guilty or not.
I would try to gather more info...find out what year is on the parking permit, get a license number and see who it's registered to (probably in the parent's names, though), etc.
Of course, I'm a wannabe spy anyway, so......
PsychTau