My former company fired a guy because the FAA essentially ordered them to do so (because an examiner was ****ed off) ...our chief pilot turned around and arranged for the poor guy to be hired at another regional.
Sometimes companies just have to do what they have to do...and the other companies know this, so they assume that you are probably an all right person and that you have learned a lesson.
The only things that could be a real problem are serious and deliberate lapses of judgement like theft, fighting, insubordination, or substance abuse.
Also, if you had an attendance problem, you will want to go to your next interview with A) a reasonable explanation and B) a plan to keep it from happening again.