Re: What extra AR parts to take to a class?
What you take would be decided by who you train with. If you go train with EAG Tactical, they have a dozen rifles you can borrow free of charge if yours goes down. Other groups do as well. If that's the case, then the minimum you would want to bring would be an extra extractor and an emergency small parts kit. Rock River Arms markets their LAR-15 "Oh Shoot" Kit for $15, which basically includes almost anything you would need if your gun went down. The only thing that it doesn't include is an extractor, which is also relatively inexpensive.
Several places carry the RRA "Oh Shoot" kit, but you can get it on their website.
http://rockriverarms.com/index.cfm?fuseaction=category.display&category_id=523
The Extractor you can get anywhere, like a gun shop or online at MidwayUSA or Brownells. If you get the RRA "Oh Shoot" kit, I would also get their Bolt Rebuild kit, which has all the needed bolt/BCG parts you'd need.
If you go to a course where they don't have loaner rifles or you aren't sure, I would recommend buying an extra whole lower parts kit as well as a spare complete bolt carrier group at the minimum.
If you plan on going to training courses on a regular basis in the future, it would be prudent to think about investing in a second rifle at some point. I wouldn't do it for one or two classes, but it you want to get serious about training, a backup rifle is a good fail-safe.
The other option is to bring cash and alcohol. I bring my armoring kit and parts containers to every course I take. When another guy has his rifle go down due to mechanical trouble, I will charge them for the cost of the parts only, but it's sort of expected that they buy me dinner or at least a round or two at the bar.
OH- Don't forget to bring spare batteries for every battery-operated piece of kit you have. Optic, light, laser, earmuffs, pistol light, etc.