Currently, if a question or answer accumulates a sufficient number of offensive or spam flags against it, it is automatically deleted and a reputation penalty is imposed on the poster. Likewise, comments that have a sufficient number of flags against them are auto-deleted. This requires no moderator intervention, and if no moderator happens to be active when this occurs, we won't even know that this happened.
These are cases that moderators should be made aware of. If someone posted spam obvious enough to be flagged heavily by the community, odds are that account (and any related account) needs to be looked into. Trolling or abusive posts and comments are cause for a strong warning from a moderator, if not a suspension.
And then there's coordinated gaming of these flags to attack others. The use of sock puppets to cast synchronized flags in an attempt to destroy content once was a purely theoretical exploit. That is no longer the case. In the last year, I've personally dealt with two users who employed sock puppets to flag and auto-delete comments critical of their answers, and both attempted to used offensive flags to destroy competing answers (one succeeded). Over the last couple of days, GameDev has been dealing with a much nastier form of this.
For these reasons, I would suggest that moderators be made aware of comments and posts automatically deleted by the community as a result of spam or offensive flags. For posts, this could come in the form of a flag raised by the Community account similar to the warnings we get about users mass-deleting posts, etc. Something like "Post deleted due to community spam / offensive flags" would make it clear what happened here. Warning flags would not need to be generated if a moderator was the one to cast the auto-deleting spam or offensive flag.
For comments, I'm not sure about the best way to expose this, whether by a Community flag on the post ("XX offensive comments deleted") or by a special type of comment flag indication in the mod dashboard. Comment notifications may also need to ignore ones that get flagged and auto-deleted based on containing certain non-offensive keywords (the "what have you tried" type comments).
There have been a number of spam, trolling, or otherwise abusive incidents over the last year that could have been dealt with much earlier if we had this kind of information presented to us. I do not believe that it would be any noisier than the other automatically raised warning flags we get now.