Teams can and should set policies for behavior by both mentors and students.
Our team has application forms for mentors and students to be submitted every year.
The mentor application includes a signed "mentor code of conduct" which not only helps remind the mentor of the age group in which he is immersed, but also satisfies an awareness training requirement for our team's NPO insurance policy.
The student application includes a "contract" signed by students and parents. The contract makes it clear that FIRST is not a substitute for school and a grade requirement is in effect for attending competitions. Within the terms of the contract, students are evaluated for productivity and can be asked to leave the team if they do not contribute. Much of our student contract is adopted from handbooks from teams like
"Wings of Fire" and
TechnoKats.
A common thread between our "code of conduct" and "student contract" is respect among team members. That doesn't mean friction never exists or people don't lose their cool. We just don't want team mates to hurt each other. "Shake hands and make up", "agree to disagree," or "keep them apart" are all options when dealing with conflict.
You ask, "What can I do to improve conditions for our team?" That question suggests what you really want to do is to help lead the team. A discussion with the lead mentor about you helping the team by organizing and tracking students' efforts is a start. Expressing your concerns to the lead mentor about hurtful actions of the "valued" mentor might prompt some changes, too.
Something to consider about mentors (as Jared341 suggests), is being imbedded in a "day-job" where performance expectations are high can make a person
really impatient with under-performers. Talented, dedicated people can become frank, "hard-headed" and darn near vicious when frustrated. Part of becoming "thick-skinned" is learning how to dish it out as well as take it. Sometimes, giving one another a hard time is a like a game. That sort of thing happens a lot - even where Dave's "Mars Cars" are built!
Good luck and realize that you're getting acquainted with the real world. Don't let it get you down.