I once worked in an envrionment like this that saw about 1k emails a day when I started... What I started doing was trying to resolve one bug a day... I'd look at an error, do a search in my email filtered folder for that error, and manually count them, whichever had the most emails, I took care of it.
About 2/3 just came down to filtering certain classes of errors. 4xx errors, I stopped email notification altogether, since they were already being trapped/handled by the system. Others were a little more specific. Ironically, .Net tends to handle some things that should be 4xx errors as 500, so reclassifying those took out a lot as well.
In the end, within about a month, the emails were down to a manageable 20 or so a day and got more visibility as a result.
About 2/3 just came down to filtering certain classes of errors. 4xx errors, I stopped email notification altogether, since they were already being trapped/handled by the system. Others were a little more specific. Ironically, .Net tends to handle some things that should be 4xx errors as 500, so reclassifying those took out a lot as well.
In the end, within about a month, the emails were down to a manageable 20 or so a day and got more visibility as a result.