First, let me link this thread from arguably one of the few people in here who actually has a clue on the process.
Then, let me reply to your enquiry by stating: dude, I haven't a clue! Some invites I've got completely surprised me and 1 particular ding did as well (still no admits for me, though). However, I'll try to get the discussion rolling (and for the record what I write is just my SWAG*)
1) GMAT influences how your app. is read as follows:
Low GMAT: Hmm, let's see if this person is truly exceptional or if I should just throw his app. in the bin right away.
Medium GMAT: Ok, let's see if this person has put his act together enough.
High GMAT: Let's see if (s)he's just a high GMAT or if (s)he has anything interesting to say.
2) There is some variability to the process. As speculated before, two identical people will not always get the same result from the admissions process. Even when I could argue that 8 out 10 times the result will be the same, the balance 2 out of 10 the result may be the opposite. I guess we're dwelving into luck here, which we all hate to admit. For eg: the first person reading your app. might be hangover from the night before or may have had a fight with his/her partner that same day. Probably if your app. is read on Monday it will have a different outcome than if it's read on a Friday. Some app. readers may have a similar background to yours and feel "connected" to your stories. Some may actually think that your Junior Helpdesk Assistant is actually a dead end job while others may interpret it as "paying your dues". I've heard adcoms mention that apps. get read by several people and all of them get read by at least one adcom. But we can't honestly think that if an app. is handed over to an adcom with a ding recommendation from a 2nd year student it will get the same consideration than an app. with an interview recommendation from a 2nd year. Luckily, my previous estimation of 8 out 10 for most applicants is quite OK. Unluckily, I have no way of finding out whether it's true.
3) "Crafting" a class. I've heard adcoms mention this concept. Adcoms admit to look into admitted candidate pools as groups, after a certain point (i.e. if you've made it past the initial cut). They can exclude or include border line cases (which I'm assuming can be as high as about 30% - 40% of admits + all waitlists), based on their estimation of future class dynamics. You know how every alumni at receptions goes bragging about being in class with "a guy who actually worked for Nasa mission control" or "the girl who climbed Everest at age 16" or whatever. No alumni I've met bragged about being in class with a very accomplished Big 5 accountant or a great Junior Mgmt consultant or IBer. They like to have classmates in "hot" industries to share advice for future job searches, but there's just no WOW factor in it.
There are probably no fix number of spots for each industry, profile, background or nationality, but most definitely a general guideline of what a "good" class profile will look like. Do I think it's fair? No, but who said business was ever fair?. Do I think it works? Yeah, it works great! Helping mostly average people to earn astronomical salaries by investing 2 years and borrowing some money sounds like a great accomplishment to me.
4) Yield Management: if you are a very strong candidate, some schools may be tempted to ding you for yield management reasons. You can counter this effect to a certain extent by visiting, contacting alumni or students and showing a better than average why X? essay. Re-applying works great with some schools, as well. You can also counter this effect by applying to reasonable schools. Too many backups? Too many dings. Too many reach schools? Again, too many dings. Portfolio crafting is important.
5) GMAT hunters: some schools looking to make a move in rankings maybe willing to admit high GMAT candidates which are otherwise weak to move their average GMAT up.
6) Diversity hunters: related to point 3) above. some schools may be struggling to keep their classes diverse enough. So they will be willing to compromise some aspects of a particular candidate (maybe GMAT, GPA or sth) to keep bragging about how their students come from 70+ different countries and speak 50 different languages (which btw, is BS if 5 out of those 50 languages are spoken by only 1 person and if 10 out of 300 people comprise 40 of those 50 languages)
7) How similar candidates have done in the past. Now this seemed far-fetched when I was first introduced to the concept, but it goes like this: Suppose you work for company X. Your position is Sr. Analyst or sth. Your numbers are competitive or school Y. Your extras are quite Ok and so are your recos. Now assume that a candidate with a very similar profile made it into the same school Y a year or two before you apply. And now assume that he has proven to be not one of their brightest stars. Either (s)he has not participated actively in the community (extras, clubs, etc.) or (s)he has been catalogued by work groups as a "free rider" and actually failed a class or two. So adcoms *might* think: "Fool me once, shame on you, fool me twice, shame on me" and ding you based on your "clone's" performance.
8) "Fit": HBS focus on leadership. Kellogg focuses on group work, collaborative spirit, etc. GSB focuses on quant skills and hardcore economics and finance. MIT has an operations / entrepreneurship aura. Columbia is perceived as a finance school.
So, first, don't complain on Kellogg dinging you if you've written essays about how you are a great fan of Nicholo Machiavelli. Or complain on HBS for writing about how you are great about humbly following orders without questioning or how you enjoy the most joining other people's initiatives. (Actually, don't complain about HBS or Stanford at all, being these the top two schools every applicant should expect his status to be "ding without interview unless confirmed otherwise by written evidence")
Second, the "fit" issue can work combined with point 6). Eg: If Columbia is perceived as finance focused, it will probably have an unbalanced applicant pool with financial backgrounds. But they'll still want to have a balanced class. So, I can argue, apply to CBS with a marketing background and improve your odds!
9) Luck: self-explanatory
10) Randomness: ditto.
11) Timing: R1 is a must for some schools. R1 or R2 is must for most schools. The year in which you apply is also a factor. Apply in 1999 with an "I wanna startup an Internet company" and you will bring no diversity to any class at all. Apply in 2006/7 and suddenly all schools are boasting increased number of applicants.
12) Be fair: no school owes us more than considering our apps. (which is what we paid for). After that, all they owe us is respecting the rules they've laid out for the process. And since the process is always officially described by schools as holistic, no candidate can honestly confirm that (s)he should be admitted. Probably the only rule schools can break is not respecting their deadlines. Apart from that, they can do whatever they like and we would not be able to judge them as unfair. We know the rules when we apply! And if we don't like them we can choose not to apply and save whatever fees they are charging.
13) I still haven't a clue: that's it. I think I've written more than enough and made no breakthroughs. I'm gonna leave this post as it is before everyone starts thinking what an arrogant idiot I am.
14) Please everyone who feels like it contribute with your views on the process.
* SWAG = Scientific Will @ss Guess