Can a mod be banned? Sure, we are subject to the same rules as everyone else on the site. However, abuse of power, like what is suggested in the op, would not lead to a ban, as it is not a rules violation. It would (and should) lead to a demotion for abuse of power. Some disagreeable calls will happen, such is the nature of humans. But if any mod starts saying things like "I don't like you" for the ban reason, well... they probably won't be a mod for too long.
Like Tor says, though, actually banning any staff member, including a moderator, takes an action from an administrator. The procedure for rules violations is the same- if a user sees it, they can report it. A moderator will look at the report, and forward it on to an admin should there be a moderatable issue. Said admin will then take action against the staff member. Sometimes it is through warnings; I know that some people feel that nothing is done about some staff members, but I can tell you that some of us do have warnings on profile.