Yeah like it was said before Enlistments are getting tougher. We are also booting out more people. About every ten years or so we go through a purge in the Army.
I've been in for 13 years (active/reserve mix) currently on active duty and will probably make Major early next year.
There's something in those tickets that is throwing up the red flag. I think it takes seven years for a criminal (non-felony) act to be taken out of your record. Even then sometimes you have to hire a lawyer to get it cleared.
One last FYI...a lot of SF operators already have their Bachelors. Out of the estimated 20 or so Soldiers I have endorsed to attend selection only one has made it.
Don't give up. Get a print out of your DMV record and make sure it lines up with what happened in court. People sometimes make fat finger mistakes...who know they probably have you listed as a sex offender? (that's extreme but possible)