As promised, a useful post! And probably a long one.
As far as rendering goes, the problem that I see people running into more often than anything else is render layers mysteriously breaking, especially when file referencing is involved. The symptoms are typically either objects disappearing or Maya simply being unwilling to switch to a specific render layer, claiming in the Script Editor that there are “overrides to a node in a missing reference” or something to that effect. A lot of less experienced or just less technical types will try to solve the problem by either importing their references into the scene (which is rarely a good idea), or by screaming obscenities (which is exhilarating but ineffective). There is a better way to get your scene to render with no problems, and be able to use file referencing. The trick is to use shared render layers properly, only allow certain edits to your references in your final scene, and make sure that your references are clean.