Well, this past year, my team was a rookie, but I was on my second year. We had close to 30 members as well. During the build time, we had 3 committees, each with it's own student leader. These committees were the Drive/Chassis committee, the Sub-Systems committee, and the Programming/Control committee. We also allowed a team member to be in any number of committees they wanted. It is a good thing if you have students that understand every aspect of the robot, they make good drivers...like me

Anyway, It worked out pretty good. We had a problem with one family on our team, however, who was trying to take control of the team over the chairman of the board (my mom)'s head. And they overstepped every boundary we put on them. For example, we said that the time limit for a driving chassis was around the 3rd week. They kept intentionally slacking off, and giving the old "Well, what happens if it isn't done by then?".
So, we implemented a Project manager. The project manager is an adult (or student, were having both this year) who oversees the entire project, and sees that things get done (closely, at least) on time.
This helped, but it still didn't solve out problem too well. They also gave us a big problem with the subsystems committee. During design time, they basically weaved a nice little plan to influence other team members with pressure to vote for their lift idea. It was way over the line, but we couldn't kick them from the team, they were housing our build area. So, without proper testing, they focused soo much on that lift. Had people straying away from the drive/chassis completion to work on the lift. I knew it would be a problem.
Aside from the fact that it ended up only stacking 3-4 bins, it put us 20lbs over the weight limit.
We removed it at competition, and it hasn't been touched since.
I would suggest that you form a good way of testing your ideas to consider weight/tolerance levels before an idea is accepted. If your'e spending alot of your time on a device, and I't putting you behind schedule, and the device won't even end up working anyway, then your'e really wasting time.
We found at competition, that even though we had a rough time getting there, we could still work as a team to get our bot going. So, we watched a few practice matches, and reformed our entire strategy. We focused on making our bot lighter, speeding it up a bit. Getting a successful auto mode going (our line-tracking was a dud), and being able to move bins well. And so, we did just that. We ended up as 90lbs of bin moving power, and we were the fastest at our regional, and one of the most powerful. Our efforts as a team landed us the Rookie all star award, and or teamwork at competition made us quarter-finalists.
We also have student leaders. Captain, Co-captain, Secretary, Treasurer, and this year, Project manager. As soon as our leaders are elected, they are responsible for running team meetings. We have a fund-raising committee that comes up with ideas, and we usually have the adult leader of that group plan out the calendar of events.
For corporate sponsorship, we put together 20 business packets. Each packet contains our Chairman's award entry from last year, a cover letter, info about first, one of our business cards, and (my favorite) a miniCD burned in VCD format with a 2 minute business video we put together last year.
We have been blessed this year with parents on our Team. One of them works for GE, and they plan on getting some of our information to them. Another works for FlexiCell, a small company of roughly 30 employees, which is in the top 3 leaders of flexible machine cells in the eastern region. FlexiCell is interested, and they want us to give them a presentation. It sounds like we may have them a a sponsor of money, machine shop, and mentors all in one this year.
We also had a fun idea to make a Robot Bathing suit calendar. We were going to get together with some of the local teams, gather some swimsuits, and get some VIP photos of our bots wearing them, then put in beach scenes in the background. We havent made it yet, but it's still in the works...