I was working on updating the FAQ Reputation requirements compared, which says that despite most privileges of 25k+ users being conferred as part of ♦ moderator rights, there are a few (4.5 technically) that are not awarded as part of it, and the check only checks for the required reputation. The FAQ on moderators also says the same thing (after I edited it). These include:
- Voting in moderator elections
- Answering protected questions
- Not being prompted to comment when downvoting (counted as half, since it doesn't actually restrict one from doing anything)
- Having a network-wide flair
- Having an expanded usercard (per Laurel's answer)
These may not be relevant when it comes to most active moderators (which are elected), but does come in handy when it comes to new pro-tem moderators on beta sites, automatically-appointed moderators on beta site pro-tem elections where they had only 300 rep (the minimum required to nominate), and (most importantly) SE staff, who have network-wide moderator rights but usually have only 1 or 101 rep on sites. The case about network-wide flairs is relevant because the list of CMs here contains flairs, and there was one case where a CM didn't have the required rep despite having mod rights so they showed up as an unsightly sad face emoji there.
Update: Thanks to Laurel I know that the expanded user card privilege is another thing that only checks for the required reputation for the "established user" privilege, and doesn't allow mods access. This therefore increases the count to 3.5, but I want to know if there are more.