Keep in mind that the severity and extent of background checks is determined by the Federal government as much as by the individual airline today. Since 9/11, the Feds have increased the list of "crimes" that will disqualify you from working in an airport restricted area.
Be honest. Even if you were arrested, but the charges dismissed, there is still a record of the arrest and the original charge. If the question says "have you ever been convicted of...", it sounds like you can truthfully answer no. But, if the question says "have you ever been arrested or charged with...", answer truthfully that you were arrested, but the charges dropped.
If it is an issue, the airline will pursue it further, but I doubt it. Good Luck! Southwest is a wonderful company to work for. I have several friends here in Dallas who are employed with Southwest, and I have never heard one of them even do normal day to day griping about their job or the company they work for.