Everybody has blemishes on their driving record. The big issue that airlines are going to have are careless/reckless driving offenses and DUI's (In other words, offenses that have criminal penalties- misdemeanor/felony convictions).

Be sure to keep your record clean from here on out- no speeding, no accidents and you shouldn't have any issues. Also, enrolling in a defensive driving course probably wouldn't hurt, plus could save you some $$$. (Ask your insurance company or the local DMV for info)