You guys are paranoid. Plugs work fine. If you're really concerned and have the time, get a patch (I'm certainly not saying it isn't better) but there's nothing wrong with a plug.
I manage to pick up nails and screws in my tires pretty frequently, and don't have any real issues with plugging them. When I first bought my (used) 300ZX, I went about 5,000 miles and then it was time to replace them. Tire shop removed the old tires, and amusingly enough there were something like 4 or 5 plugs in one of them. And they survived plenty of 300 horsepower burnouts and 140 mph runs for the border. So I'm guessing that in most cases, a plug will do just fine. I think over the last few years I've put in 3 or 4 plugs and one patch, because that time a HUGE cement screw went into my tire.
You do run the risk of off-balancing the tire with a plug, but if they patch your tire they definitely have to rebalance it immediately afterwards. But of course for a patch the tire is already off the car. I've never used the DIY kits, but had plenty of gas-station-mechanics put plugs in, and never had an issue. I can't comment on the tire rotation, because I've never rotated my tires before. (for various reasons, not possible/needed with my vehicles)