There were several, but most involved Saren Arterius.
This turian spectre was resolutely opposed to humans in general, never mind human spectres, and had gone so far as to sabotage a mission of then-candidate spectre David Anderson to scupper his chances - twenty years prior to the events of Mass Effect.
Saren's misanthropy became even more pronounced when indoctrinated by the Reaper vessel he inhabited. Shepard of course was trying to pin the blame for much of the geth war on Saren, which did not help his own spectre candidacy - until he found proof.
It wasn't so much a "Shepard" problem as a "human" problem. Granting humanity their first Spectre would be yet another link in the chain of recognizing the Alliance as a galactic great power, which was met with some consternation by more established races. --luper567