I'm going to answer the first part of my own question.
After upgrading my iPod Touch to iOS 5, Location Services started working again. Not only did it start working, it's showing the location as a point in the street in front of the house.
1) The location I manually submitted to Skyhook in 2009 was in the street farther south, by the mailbox, so the old data point is not being used. Not suprised since I have no reason to believe that Apple went back to Skyhook. A visit to Skyhook's website verified that this point has not changed.
2) The location that Apple started using last year was a point on the main highway 1/2 mile east of here.
So somehow Apple has independently obtained new data about my wifi location. It's possible that during a recent party, somebody with an iPhone had connected to my Wifi and that data was sent back to Apple. It's also possible that a Wifi data collection vehicle drove down this road. It's very rural with only three homes on a one mile stretch, so although possible it's difficult to believe.
It was my previous understanding that Apple started requiring that devices be within range of several Wifi signals to improve Location Services accuracy. Being in a rural location, it's nearly impossible for my iPod to pick up any Wifi signal other than my own. With Skyhook, this was never an issue.
However, iOS 5 seems to heavily depend on Location Services so maybe they've changed something critical to how it functions in order to improve accuracy without requiring multiple Wifi signals.
I'm going to accept my own answer. If anyone has a better answer to my original question, I'll consider accepting that instead.
That is normal behavior. Each reinstall of settings on a clean device requires a reboot. It doesn't matter if the device is 'clean' due an iOS upgrade or clean from a security wipe. iOS backups are not simply copied over. They are interpreted for security and compatibility.
Have a look on the device next time you upgrade iOS. It should perform two reboots. One for the iOS and one after your settings are in place.
Oddly, he should have don't that second reboot on his own since its part of the procedure.
Best Answer
Apple works very hard to conserve battery life, and determining location, no matter if it is through GPS, cellular, or wifi connections takes extra battery. The arrow displays any time a 3rd party app requests your location. For instance, when you open Maps, the arrow will likely turn on because Maps needs to pinpoint where you are. The arrow may also turn on for system level locations services (settings can be adjusted in Settings > Location Services > System Services), and depending on your settings, the arrow may or may not appear for that.
As for Location Services being on or off, you can set that in the settings (Settings > Location Services), but if you see the arrow, it is likely on already.
The arrow only appears when location services are active, and may or may not show when it is just on.