If it isn't for a TS I doubt it would be an issue. Was trespass in a B? I knew people who have done a lot worse but still gotten a clearance. Are you mil or civilian?
Your Misdemeanor Arrest will not be an issue for a National Security Clearance. What WILL be an issue, is if you lie about it. They want to determine how honest you are. They WILL find EVERYTHING about you, so just tell them everything up front. That is what will impress them.
BIG PLUS on that also . Never lie on Security Application because chances are, it will come back on you . My younger Brother even had a conviction back when he was younger . He was stait forward with all Info & he got Fed. Sec. Clearance for some employment .
The Best way to pass a Lie Detector is. Don't Lie . .
There is a BASE Jumper that did not make into a federal agency because of BASE Jumping. Squeaky clean record, incredibly intelligent, was all the way through, but BASE killed the job. I am sure he or she may chime in on this if they see this post.