Currently, moderators cannot see quickly exactly which privileges a user who has flagged actually has. As described in this answer by animuson,
when reviewing flags, we don't see your reputation. Without opening your profile, we have absolutely no idea what privileges you actually possess.
In the linked question this has lead a moderator to advice a user to do something he/she doesn't have the privilege to do.
My opinion is that moderators should see the relevant privileges, as it is important when writing out a response. New, low-rep users take what moderators respond to flags for granted, and if the advice is wrong due to grounds that user hasn't got enough privileges, it's a really mixed message that will lead to unneeded frustration.
Here's another recent example where lack of seeing the privileges has lead a moderator to do a wrong decision.