It can't be an easy process. As you know if you've done the Shattrath tour, doing quests for Aldor lowers your reputation with the Scryers, and vice versa. And there are three levels of hate for each faction-- you start at Unfriendly (depending on which faction you first chose to join), and then slowly fall down to Hostile, and then Hated. You can't actually get the normal rep quests for the other side until you reach Neutral, so if you want to switch sides, you have to go to Shattrath and get a special quest (for Scryer rep, it's Voren'thal's Visions, and for Aldor, it's Strained Supplies). That quest consists of a simple animal drop (basilisk eyes and spider venom sacs, both from Terrokar), and can be repeated all the way back up to Neutral.
Coraline says it's not actually that bad-- she went from Hostile to Unfriendly within about an hour of farming (which means she still has to fight to Neutral to start doing the normal quests). People working back towards Aldor are able to get silk from the spiders (that sells well on the AH), but unfortunately for repentant Scryers, the basilisks don't drop anything really good. They do drop Chunk O'Basilisk if you're a cook, and they can be skinned if you're a leatherworker, so there's that.
Anyone else made the tredge back between the Aldor and Scryer factions? Coraline doesn't say she did this, but I would: if you're leaving your faction, make sure to grab all the goodies you can. I would be completely impressed to see someone dual-wielding both the Vindicator's Brand and the Retainer's Blade at the same time (you don't actually need the rep to wield them, do you? Just to own them, I'd assume).
Update: We've got confirmation-- commenter shooter's guildie shows it is possible to wear both Aldor and Scryer gear at the same time. Could be a bug, but if you want to grind both factions for all the rewards, it seems you can do it.