Against Graham, the argument (lame it is) goes like this ...
Coaching a judicial nominee behind-the-scenes is not the proper role for a Judiciary Committee member who must subsequently sit in judgment on that nominee. Indeed, it could be a violation of the ethical duties of a senator. Here's what Senate Rule 37 (Conflicts of Interest) in the Senate Ethics Manual says:
"No Member, officer, or employee shall engage in any outside business or professional activity or employment for compensation which is inconsistent or in conflict with the conscientious performance of official duties.'' ... The Committee has interpreted this paragraph to prohibit compensated employment or uncompensated positions on boards, commissions, or advisory councils where such service could create a conflict with an individual's Senate duties due to appropriation, oversight, authorization, or legislative jurisdiction as a result of Senate duties.http://thinkprogress.org/2006/01/09/graham-ethics/
The unspoken argument is that Alito will not be idependent when matters involving exexutive prerogative get to SCOTUS, e.g., FISA/NSA, detention of enemy combatants.
Don't you think that the word "compensation" is the kicker though...
Graham was hardly a "paid" moot court participant.