I would say that for me the biggest stumbling block that I have, aside from theological ones, is the sexual abuse scandal. I live in a heavily Catholic neighborhood, and two of the closest parishes to me have been affected. The first had two of three priests removed due to accusations of abuse, and the second had a priest arrested from a sting operation; he was going to meet with a 16 year old girl for sex, and they found child pornography on his computer. The abuses also seem to be very wide spread, with new accusations recently coming from Ireland and Germany. What troubles me most isn’t the abuses themselves, terrible though they are, but how the Catholic Church (CC) has responded to them. It seems to have been the policy for a long time to keep the issue within the CC and not to notify the police; priests were given counseling and moved to a different diocese where the abuses often continued. The counter argument I’ve heard is that every church has priests that commit sexual crimes, not just the CC, that the number of offending priests has been exaggerated, that the CC never really tried to protect the priests or forbid notifying the police, etc. I’ve just never found these counter arguments convincing in light of some of the documents that have surfaced about how this was handled in the past in contrast to what the CC claims it did. I just don’t see this problem happening as frequently in other churches, in particular child abuse. I believe that it’s directly related to the practice of clerical celibacy; priests have no acceptable sexual outlets, and it seems to manifest itself these in these abuses.
The Crusades, the Inquisition, and Indulgences are also issues for me, but in particular indulgences since they’re officially approved of and practiced.