For obsolete or too-chatty messages, you can flag one with a custom flag describing which ones need attention, or flag them each individually — whichever is more convenient for you. (That includes “selfishly” individually flagging comments because “I want more helpful flags!” — after all, you are identifying multiple comments that you think need attention.)
The tools on the moderator side are pretty well designed to handle whatever people throw into the flag queue in a way that isn't annoying for the moderators. They have to be — these same tools are designed for handling the firehose of flags that Stack Overflow mods get! For example, all flags for comments under the same post show up as one notification/“ping”, and as one flag-handling “job”, making it easy to review and navigate even when there are lots of flags under multiple posts. So you don't have to worry about flooding us, even with many flaggable comments on one post. We can take it! We get astronomically fewer flags than SO.
Handling (as opposed to getting notified for or viewing) one or many comment flags is also pretty similar in practice, since deletion = accepting the flag, and usually that's what was going to happen regardless of whether it's was one flag or many that drew our attention to the comments.
The exception I would urge is for “bad” flags, like rude/offensive: those get noted on an account (for human reference only), so it's useful to have those actually flagged individually even if your preference is for one custom flag. (Usually “bad”-flaggable comments come in singles or low single digits anyway though, so it's rare that you will need to decide between many or one flag. Thankfully!)