If your a non-mod, you can take it to another moderator, or take it to the meta site if there is one, or contact the admins.
Really the answer to many questions about moderator problems, is Advice. A moderator is part of the moderator team, and if the moderator team cannot act as a team then the site has a big problem.
If some action needs to be taken on a user, and another user does the same actions as the other then both should have equal action taken on them. If a moderator does not do this, then he should be advised, and if that was done already then he should be warned strongly.
Some actions the moderator team can take that may prevent the moderator kicked off the team (if he is valuable) are:
- Tell the matter to another moderator.
- Advise the mod. Easy
- Identify those users who he favors, and another moderator takes care of them before he/she does. Hard
- Warn him. Easy
- If there are admins, you can take the matter to them. Easy (Unless you can't contact them)