As just a raider in what I feel is a very casual guild. The application process is something that goes unlooked by alot of people in a casual setting. I know I for one will always admit I am not an expert in any class other than my own but one of the big things i do look at is their UI.
I'm almost positive we've all raided with that 1 person who habitually makes the same mistake, and you sit there and wonder, "What are they looking at?" For example, I feel alot of people have a tendency to play with DBM straight out of the box. They don't take the time to configure their bars and warnings, so there's just a bell and whistle going off every few seconds and it gets to the point where it becomes white noise. I know DPS have a tendency to make their recount 1/3 of the screen for whatever reason. I never understood that. DPS also have a tendency to clutter the middle of their screen with superfluous scrolling text. Healers do that do that as well, especially the ones who don't use an combat text addon so they see their hots popping up everywhere. Again, I don't think what I'm saying is necessarily canon but I think it helps.
Another aspect from the level raiding that I'm at is their rotation and to an extent logs. If they have seasoned logs from an established guild I think that''s more or less the end all. You can see their "good" nights and "bad" nights. We've all had our off nights from time to time and to judge someone based off of one night i don't think is necessarily fair. That being said, looking at their uptimes and overall activity can definitely clue you in on what he or she is doing. Speaking from personal experience the guild for example, recently received an in-house app from a "non-raider". This person did not have logs but i feel a comprehensive breakdown of their rotation I think would've sufficed. I'm not just talking about "Hitting A then Hitting B Then Hitting C", I'm referring to a rotation in terms of variables and what you would do in specific situations along with your basic rotation.
What I think is the deal-breaker is their reaction to the criticism. I think guilds especially 25mans who are perpetually recruiting but are always looking for that, "healing monk, or that awesome resto shammy, or even that really good fire mage", something very class specific. What I've seen some guilds do is get really excited and almost bypass the entire app process just b/c X class happens to be on the app forums. Letting an app ripen on the forums I think is a good thing but letting an app rot on the forums is not. Finding that balance is hard though. To bring a close to my ramblings by the way it's not so much the app because there so much grey matter in terms of what each guild wants and looks for. I think what the overlapping underpinning is, exposure. Exposure to the rest of the guild via comments made, resident class advice. "Hi I'm the resident warlock, etc etc etc......" other constructive comments made, as much as the app process is made for the guild to get to know the applicant it's a two way street.