No flats on my LT so far. However, the front tire is a lot narrower than the rear, so that right there would probably mean a 3x more likely to catch a nail etc. than in the front, all else being equal. Which, I'm sure, they aren't.
Thinking about my experience on cars, most of those have been in the rear as well, though several were, I suspect, "planted" by people I had pissed off.
As for a magnet ... well, the problem is, magnetic fields fall off RAPIDLY with distance. If you have something that doesn't impact the ground clearance of the bike, you would probably have to have a near super-conducting magnet to pull a nail off the ground. If you were willing to dangle something movable (the mudflap idea) an inch off the ground, you could probably get by with some nice passive "rare earth" magnets. If you know anyone in the IT business, they probably have a large collection of them harvested from dead/obsolete hard disks. Also...IF you pull a nail off the ground, it has to be fully captured by the magnet at 70+MPH -- not just oriented upwards in a perfect position to plunge into the rear tire as it comes by, or pulling a nail that your rear tire would have missed a little closer so now you DO hit it. Also...if it is on a mud-flap like thing, when you hit a bump, the flap will bounce up...and probably stick to the bottom of the bike and stay there.
Electromagnet...I don't think you would get enough pull with the power available on the bike -- plus you'd be horribly impacting your gas milage by sucking a lot of juice from the alternator. (hm. however... maybe a large electromaget, not constantly engaged, but energized by a large capacitor for a fraction of a second every time it detected you driving over a metal object, the object gets pulled up, and a (relatively) small permanent magnet holds it until you stop.) Of course, you could drive over a washer and have the zipper of your boot ripped off! Ok, I'm over thinking this now, I must stop.
Another problem with the magnet idea: it only works with magnetic materials -- aluminum, brass, stainless steel will still be making a beeline for your tire.