"I've seen odd mapping glitches on phones (my Blackberry in Beijing had Google Maps consistently shifted about a city block or two in one direction), "
Yes, many devices like this have an accurate map database, but the registration of the map is consistently off by about a city block or two in one direction. It will show you driving off the Interstate highway and going parallel to the pavement by a block or two. That is frustrating. There are things that cause that, and some of them are user-correctable and some are not.
Refer to the topic: GPS Datum. Learn what that is and what it does.
Also read up on the topic: GPS Blunder. Learn what that is and what it can do to you.
If you understand how GPS works, you will find that when the receiver sees the multiple satellites, it determines a PVT solution. That means Position, Velocity, and Time. In all likelihood, it will determine two PVT solutions, and one makes sense and one does not. One will be within 300 miles of where it had its last fix, and it will be somewhere reasonably on or near the surface of the Earth. The nonsense solution may be too high in space, or going at some incredible velocity. Nearly all of the time, the receiver will guess which solution is nonsense and it discards it, so the only PVT solution that the user sees is the accurate one. However, once in a while, the real solution and the nonsense solution are moderately close to one another, and once in a great while, the receiver guesses wrong. This is called a GPS Blunder.
One day I backed my car out of my garage in Silicon Valley, and I gave the GPS receiver a moment to lock a position fix. Suddenly it displayed me traveling about 20 miles away, going at 400 miles per hour, and flying over the foothills. For the first five seconds, I stared at it in disbelief. Then I shut the receiver down, counted to ten, and then powered it up again. This time it displayed me about 30 miles away, still doing 350 miles per hour. Wow. So I shut it down again, counted to ten, and then powered it up again. This time it displayed me sitting about twenty feet from my garage and had zero speed. Ah-ha. It worked great the rest of the day.
These GPS Blunders used to happen maybe once per year, and it was purely a fluke of luck. I haven't seen so many lately, and I think that has to do with the maximum constellation of satellites being present nearly all the time now. In other words, the system is better now.
Additionally, if you happen to wander into an area of high radio-frequency fields, your GPS receiver might go squirrelly. I've been to many microwave radio sites, and the GPS would be crazy. I would leave the site, and the GPS straightened out immediately. I've been to places where I could stand at one spot, and GPS would fail. Then I could move five feet to the right, and it would work perfectly. This has to do with what we call RF Interference. Be on the lookout for anything that looks like a big microwave dish antenna. For this reason, you don't want to place a geocache near a microwave antenna, because maybe nobody will be able to find it.