If you have an arrest, whether that resulted in a conviction or some other form of disposition or a conviction which was later expunged (or anything like that), before getting mixed up in a GE application, get your paperwork in order.
This means obtaining attested or certified copies from the relevant court of the paperwork showing the entire history of the case, including a final disposition. It is often known as a "docket sheet" but it may have many other names depending on the court. It is this last piece which is often missing from various databases.
People are sometimes put off by the cost of obtaining attested documents, but the problems people encounter with GE can occur in many other personal and professional situations. As others have found, even the best kept records are destroyed for lack of space, fire, flood and the like.