In general, the background checks are for those who will be in close proximity of a protectee, or working in critical areas, or on/with certain equipment.
Examples: airport mtce/ramp crews at airports, volunteer motorcade drivers (not staff, but oftentimes there are more 'dignitary visitors' participating and they need drivers - and I've learned over the years it's usually coordinated by the political party in that area), etc.
For yesterday, names had to be run for the speakers on the stage (ok, except for the Gov and Senators, LOL...I mean the fire association representatives, chaplain, etc), the cargo elevator guy and alarm system guy for Baylor, and then the family members and fire association coordinators that were meeting in a room afterwards. In addition, normally there are photo ops set up in advance (a set number on each departure), and those people have to have had their backgrounds checked. That is different than any unscheduled photo op. Just as with many disaster areas, and spontaneous stops, no not everyone has had their background checked.
Disqualifying info is normally due to violent crimes and/or threats. We don't care about DUI's (well, except in case of a motorcade driver!), most drug use, misdemeanors, even old felonies, etc. It really takes a lot to get someone disqualified, but we need to check just to be sure. Yesterday's one that I needed higher up approval for was because he had a conviction for Prohibited Weapons, an Agg Assault with serious bodily injury (probation had expired), and he was currently on Parole for a Burglary of a Habitation. The issues: current Parole, and his weapons and Agg Assault in the past. He was allowed in, but the staff there had him flagged and knew who he was.