What, if any, roads are open to graduate schools for athletes with borderline grades? My understanding is that colleges with sports programs will admit students with "low end" but not "off the charts low" grades if the respective sports teams want them. By this, I mean grades just above the "cut-off" for admissions, without having to make a special case or allowance for the athlete.

Suppose a certified athlete tried to get into a graduate program with similarly minimum grades. To take an example, suppose the Yankees shortstop Derek Jeter retired, went to college, and got something like a 3.3 GPA which is the cut-off for certain graduate school programs.

What constituencies (if any) might such a graduate applicant have (e.g. celebrity value)? Or are "athlete" slots open only to undergraduates?
I'll answer based on the U.S. (which is where these issues are most relevant, I believe).

There is no special consideration for athletes in graduate admissions.  Undergraduate admissions are handled by admissions officers who often use all sorts of non-academic criteria, and recruiting athletes to play for the university is a specific goal at many universities.  However, graduate admissions is done by departmental committees made up of faculty, and the non-academic criteria that play an important role for undergraduates (well roundedness, extracurricular activities, athletics, etc.) are irrelevant.  If anything, a continued desire to participate extensively in high-level athletics could be considered a disadvantage, since it would take time away from academics.

If Derek Jeter wanted to go to graduate school, I'm sure some faculty would be impressed by his fame, but they would also be careful and skeptical in evaluating his qualifications.  In any case, there certainly wouldn't be a special admissions slot designated for an athlete.