1.Don't spell like a moron
Yes, yes, it's the Internet and spelling and grammar aren't cool among the kids these days. Nevertheless, you're trying to impress these people, so at least make some effort to not type like a monkey undergoing shock treatment. Typing in all lower-case with no punctuation except for "lol" makes the guild officers think that you're going to be a nightmare to have in guild chat, and they're probably right.
2.Use the actual guild's application
Not a generic application. Not another guild's application. ESPECIALLY not the application of the archnemesis of the guild you're applying to. This is usually an automatic disqualification -- if you can't take the time to fill out the application, how are you going to abide by the guild rules?
3.Don't flirt or post pictures
No one cares that you're a girl. Really. No, really. They care about how well you can play. If they ask for your gender, it's okay to tell the truth, but including revealing pics or a link to your myspace in your application screams "In the future, I will carry on an ongoing flirtation with several guildmates that will eventually destroy the entire organization." I would assume it's also verboten for a guy to flirt and post half-naked pictures in his guild application, but honestly I would probably /ginvite that person just to watch the chaos that ensues.
4.Don't complain about your last guild
Even if the split was really bad, just say "there were some issues about _____ and I decided to move on." An epic description of the drama in your last guild makes you look bad, and some of the officers in your wanna-be-new guild probably have friends in your old one.
5.Don't talk about what they can give you -- talk about what you can give them
I have seen many guild applications where the reason for joining boils down to "I want to get gear and you guys are progressed!" Sure, that's probably the real reason for it, but it's considered tactless (kind of like saying "I really need some money" during a job interview.) Instead, talk about your desire to see new content, meet new people, and help your guild in new encounters. Don't mention gear at all, really.