that seems to suggest that there was no disposition entered, likely because no charges were ever pursued. you could confirm that by calling the court in the jurisdiction where this occurred; trespass would likely be in the municipal or district court in that town.
as to the second part of your question, its not clear what you are asking. i can imagine that it could be a problem with some potential employers, who want to know for sure that there is no conviction. it could be a problem if trying to cross the border into Canada, should the border agents run a record check (which they apparently do at random) - the individual agents have great power to decide who can come in and you might very well be asked to provide proof of a dismissal (by certified court record). but it is unlikely that it means that there is an open charge for your arrest.
Sounds like you were charged but it was dismissed. You need to check with the court where it started and see what the specific status of the case is. Then assuming it was charged and dismissed ask the clerk for paperwork to vacate/expunge it from your record so that no mention of the arrest is available any longer. You may be able to handle this yourself and not pay an attorney to do it for you. If it is more complicated than this you will have to hire an attorney to help. Good Luck