Can you still get a passport and still travel anywhere and everywhere if...?

so heres the short story... boyfriend got caught speeding and they found some weed on him... he was not convicted but was sentenced to community service which he did... He said that it should be thrown out on him but he believes that there is someone on his record of this incident happening... I wanna go travelling and of course want him to come with me! He doesn't have a passport but I'm trying to get him to get one but he thinks this will be a problem either getting his passport or entering the states or somewhere. I say because he wasn't convicted and its suppose to be thrown out he won't have an issue... Does anyone know who is right??