tclassick- You should feel completely safe in RVSM airspace, because, you are. The aircraft and crew are held to extremely close expectations and any deviations will result in immediate action from controllers. In order to even fly RVSM the a/c must have at least 2 functioning altimeters, an autopilot (and use it) and may not deviate any more than 300 feet from assigned altitude. That is a MAXIMUM allowable deviation. The autopilot is expected to keep it less than 65 feet. Anyone that can’t comply will be asked to leave “the sandbox” and fly at a different altitude. There are a few more rules as well, but these are the basics… I’m sure the others will chime in with anything I missed.
If you have never seen another flight pass as close, it’s probably because GPS keeps most a/c on airway centerline fairly well and therefore not visible out the side windows except at intersections.
As for the SLOP thing, I think that’s mostly when you’re out of a radar controlled environment (as was mentioned a la Mid-Atlantic)