That being said - not sure if by room you mean one of the 3 live chat rooms that contain up to 20 participants each at any given time, or if you mean the various forums such as this being the Community Help room.
The quickest way to get the staff's attention in regards to any problem here on CM is to open up a help ticket by clicking on the gear in the top right corner of the blue toolbar within the CM page. On smaller screen devices there may be a square icon with 3 horizontal bars that when clicked on pops up a menu where the gear icon is listed last in the menu.
In short though the moderators here are volunteers, and participate just like regular CM members in that there is no particular time they may or my not be on if I am not mistaken.
With the exception of the gender-specific forums, the moderators moderate all the forums. It has been quite a while since I was in the chat rooms, but the last I knew there were no moderators there.
The best way to report forum problems is to use the Report Post function (under the gear menu to the left of the Reply button when viewing forum posts). This posts a report that is visible by all the moderators and staff. Problems in chat need to be reported via Help for the CM staff to handle.
I can't speak for the other moderators, but I don't mind if someone send me a personal message either as a heads-up that a post has been reported or to ask for feedback on something. As Dave noted, the moderators don't have assigned shifts, so if none are actively in the forums at a given time, a heads-up message may expedite response to a reported problem.
Does this help?