I don’t think Tom Riddle would show up on the map, as Dumbledore drew a circle around Quirrell and presented him to the Hogwarts Security System as “The Defense Professor”. I’m guessing the map just taps into that system, so that is all they’ll see. It could be the constant one, as all the others show up by name. but I’m not sure they’d make a fuss about that.
As for the intermittent, I’m guessing it’s Harry when he wears the Cloak—It is explicitly said that it doesn’t just turn you invisible like other cloaks, but hides you completely (except for the eye, apparently).
My other candidate for the intermittent one is Time Turned people, but since several students have Time Turners I’m guessing the twins would figure it out eventually. More likely, it just shows the ‘current’ version of the person.
...Actually, if that were the case, the map could be used to figure out which of the copies isn’t time turned. Not sure what you’d do with that info, though.
This list has been compiled on reddit some time ago. It goes up to chapter 85. Some things have been resolved since then.