good question, i would like to know this as well

The benefit of applying early: if you're one of the first to trickle in, they have yet to set up a system for handling your stuff and it gets stashed on a desk somewhere, where it never joins up with the rest of the applications and is never reviewed. Happened with the portfolio of a friend of mine this past year.

.mm

I worked in an admissions office at one point during college, and also was a student rep on an admissions committee in grad school. 85% of applications to all programs arrived within 1 week of their deadline. The only things that could be done with earlier files were to sort, label, and file them. They also had the benefit of being perused by work-study students and various faculty and admin who wandered into the office, so those portfolios could potentially be a little worse for the wear before they ever got to the admissions committee table.
The department heads and admissions committees don't ask for or do anything with early applications - in fact they rarely look at any materials until about a month after the deadlines (which gives the clerical staff time to make files, spreadsheets, send postcards requesting missing materials, wait for fall grades to be released for those applicants who are currently in school, etc.)
One thing I noticed in the admissions office is that people who sent their applications early were often people who had applied in previous years. My interpretation of this is that they might have needed less time to prepare because they were sending at least some of the same materials back in again.
I don't think sending your application early could hurt - except maybe in MMatt's scenario - but I don't think it will help either.

Interesting. Any one else work in the admissions office?

bloopox, do you know if thats the same situation for undergrad admissions?

With undergrad admissions, because of the sheer volume of applications and because most schools operate by sending all undergrad applications to every program to one main admissions office prior to sending them to individual departments, there is more "processing" that goes on in the admissions office. This is usually done as each application comes in. Materials are sorted, applicants are contacted if their applications are missing materials, their GPAs and test scores and such are entered into their files.
In some schools the undergrad admissions offices handle the entire process - meaning there is no direct departmental involvement in admissions. In other schools the admissions officers screen applicants for any minimum requirements that may be in place, then direct materials (and portfolios if applicable) to the committees of the various departments where department-specific committees make additional reviews and cuts.

I am not aware of any way in which sending in materials early would benefit anyone - either in an undergrad or graduate admissions scenario. There may be other ways in which things are handled in other schools though.
I know that it can sometimes work to some students' advantage - especially with small programs/schools - to become known to people involved in the program - for instance by attending fall open house, sitting in on crits, attending lectures, approaching people to ask questions about the program and such. There's no guarantee that this will help with admission to the program - but it has a better chance of getting you noticed than sending in your application early just to have it sit in a file cabinet for a few months.