One plan is used to cross check the other. I'm fortunate enough to have a moving map display, albeit a very basic one, which can usually be zoomed out to show the whole flight.. If the moving map track lines don't match the chart lines, that's an instant "stop" signal.
In the IT world, whenever we make available, or transfer a large file, some form of checksumming is used. Heck, even the smallest Ethernet frames use them. Because we know, from experience, that various electromagnetic influences, from somebody turning on the vacuum cleaner to cosmic rays, can flip a bit.
So we add up all the bits in the file or transmission, either using a simple addition, or using advanced cryptographic algorithms, and transmit the result of that calculation as well. The receiver does the same thing and can thus be reasonably sure that the information was transmitted correctly.
Other stuff like International Standard Book Numbers, Bar codes, SSNs and such, all have some form of an internal checksum built-in as well.
I find it amazing that flight plans, when transferred from one device to another, or even lat/long positions, don't have something like that. Obviously when hand-calculating lat/long positions or a plog, this will be a very hard to solve problem. But I've seen loads of pilots that create a plog on their PC using some navigation program, then hand-input it in the GNS430 mounted in the plane. If the PC navigation program would calculate a checksum over the individual waypoints and the complete route, and the GNS430 would do the same thing, the pilot couild then simply compare these numbers and be pretty sure that the plan is in the system without errors.
Likewise, airline pilots still get their plog as a paper printout from dispatch, and need to input it in the FMS manually. At least, that was the case last time I sat in the jumpseat of a 737. No checksumming used whatsoever, as far as I can see, so the P2 needs to check manually that the P1 inputted each digit exactly as intended. Not that much of a problem when flying airways within Europe (lots of checks inherent in the naming of airways, navaids and intersections) but it might be a big problem when flying North Atlantic Tracks.
At the moment I'm not even aware of a standard for doing checksumming in the aviation world. Let alone of an actual usage.
Not every aircraft has a servicable AP Peter, will admit the swept wing operators are more adverse to going without it compared to the turboprop pilots. Everyday in europe there must 100's of aircraft flying with U/S AP's.
Isn't a serviceable AP a requirement to enter RVSM airspace?