As with the mentee, there are few significant downsides for mentors in carrying out the role, if they do it well, other than that this is yet another demand on their time. For this reason I generally advise new mentors to think very carefully before committing to more than one or two relationships, or they may not do them justice. Some of the other downsides I have observed over the years include:
the breaking of confidentiality by the mentee (largely the mentor's fault)
resentment on the part of direct reports that they are not receiving similar time and effort invested in their development to that the mentor spends with the mentee
loss of face when a succession of mentoring relationships fail (usually a sign of poor mentoring, but occasionally the result of a run of circumstances)
having an overdemanding mentee (my favourite is the young graduate who came to see his mentor several times a day for reassurance - it took a threat by the mentor to throw the graduate through the window to stop this behaviour - by which time the relationship had nowhere to go!).