One of the easier ways to distinguish an older character from a reroll or alt is the presence (or absence) of a Feat of Strength. Feats of Strength, remnants of "the past glories of Azeroth," are among the most difficult achievements to get, and that's when they're even possible at all. Most, like the presence of an old-school PvP title, one of the original 100% mounts, or the Vengeful Nether Drake, are impossible to get these days, and are a sign that the person who has them is an experienced player. But with a little luck and a lot of elbow grease, even a new player can accrue some of these supposedly "past" glories.
I started playing WoW shortly after Burning Crusade launched and didn't expect to have a shot at most Feats, but a surprising number of them are still available. After getting The Fifth Element recently and being surprised to discover that: a). It's a Feat, and b). The original quest isn't even in the game anymore (man, I'm glad I'm such a quest packrat), I started nosing around the list of Feats to see what else a player could do even if they're new to the game. Moreover, there are two achievements you can get right now that will become Feats in 3.3, so let's get cracking.