This is more of a nuisance than a real show stopper, but given that it's probably a quick fix (a tweak of a variable somewhere), I figure it doesn't hurt to ask.
Currently, the throttle on moderator messages is you can only send one every 30 seconds.
A lot of times, when there's a sock ring or anything that warrants a moderator message for multiple people, I've already spent a considerable amount of time doing the investigation, and I have a number of tabs open to profiles ready to send them out.
However, after I send the first one, I have to wait 30 seconds to send the next one. But usually, during that thirty seconds, I have other things to do, may be distracted, etc, and I might miss sending out the mod message.
Given that for any one site, there are only 15 (that's the max number of moderators for any site, which is Stack Overflow) people max who are going to use this (also add employees of SE), it's still a very low number of people to place such a limiting, large throttle delay on.
I recommend that it be removed, or, made very, very small (allow me to perform this action every one to five seconds) so as not to interfere with the workflow of the moderators.