Lesson 6: Friendly Fire
Speaking of capturing the flag: if friendly fire is turned off, feel free to pelt any flag you're defending with an artillery strike. It'll play havoc with your ability to target, but enemies aren't likely to get through the shelling to take advantage. For this reason, in close matches it can really pay off for someone to save an artillery strike until the last ten or fifteen seconds.
Lesson 7: Dogs of War
Whether you rack up seven kills and unleash the hounds, or someone else on your team does, follow any German Shepherds you see. Their keen sense of smell will lead you right to any enemies, who will most likely be too busy dealing with the toothy menace to fend off your lead salad.
Lesson 8: Preventative Measures
Want to make life miserable for the opposition with Tabun gas grenades or signal flares? Make sure those tools don't backfire and cause your own death by equipping a gas mask or a pair of shades, and go to town. Similarly, watch out for opposing forces equipped with the distinctive headgear and eyewear: chances are this is exactly what they're doing.
Lesson 9: Second Man Survives
Don't just head straight for objectives like a guided missile: chances are they're covered. Unless you're part of a well-oiled machine of a team, chances are at least one of your own will do exactly that no matter what anyone else says. Let him go through first. The enemy will give away their position, and you'll still be alive to deal with them. This is especially important for modes where respawns are limited or nonexistent, like Search and Destroy.
Bonus: Nazi Zombies Co-op
Want to make it higher than the single digit rounds in Nazi Zombies Co-op? Remember this: the more areas of your stronghold you open, the more entrances you have to guard. By all means, open the door with "help" scrawled on it to give you a nice choke point and gain access to the mystery box, but don't remove the couches from the stairs until you have no other option for (temporary) escape.