You're not likely to get any hassles from immigration. As for the police, you should be OK. The precaution you'll have to take with them will be to a) avoid as discreetly as possible and, b) if they do engage you, cooperate at all times and never be argumentative in any way. If you have a legit problem with an American officer, take it up through legal channels AFTER the incident. Never during. That is a sure way to escalate.
Follow the rules above, and you'll be fine. Road trips highly recommended!