My DH wanted to do it, but the one thing that's put him off is the time you have to spend in the airports etc doing baggage checks etc etc. There's no guarantee you won't be stuck in that job for 5-10 years if the better positions don't come up.
DH wanted to go into the boarding parties specifically, but you have to start with the basics and that didn't appeal to him. So he's staying in the army which suits me just fine (better perks!)
The pay is pretty good though. Shift work is the thing that gets me - I couldn't handle a DH that did shift work, I'd rather him home or gone, and definitely not nocturnal
As your DH wants to join the police, I would think customs would be a good second option. I guess he would really just have to research how much time it takes to get where he wants to be in customs as there are so many different departments and roles as a customs officer.