I also saw people complaining how Megaupload didn't take down some files, even if someone reported them as pirated content. However, only copyright owner is able to fill a proper DMCA notice. You can not, as a random citizen, submit a DMCA notice and expect the file to be taken down. Let alone just reporting a 'pirated file' via email.
There is a lot of copyright management companies out there that do the work for the *AA. There is no provided way to validate a specific takedown. Say you run a site like MegaUpload and you receive a takedown notice from a gmail account. Could you really beleive in the email as being done in good faith? What about all those companies that don't even take the time to publish SPF records.
As reported by MegaUpload, 70% of fortune 500 companies had accounts linked to them. How would you sort out what is infringing from what isn't? It could happen that works in progress and final works get distributed internally that way.
What about remixes?
As for just having a bunch of regexes, Hotfile lawsuits against Warner show how it can fail (see: http://arstechnica.com/tech-policy/news/2011/09/hotfile-turns-tables-accusing-warner-brothers-of-dmca-abuse.ars )
There is also the the matter of volume. In the indictment, it says that Carpathia (a hosting provided) provided 25PB to megaupload. This would be a lot of files to verify. And even then you could make a lot of false positive and a lot of false negative. It is not specified how much data capacity was at Leaseweb, however the amount of servers was similar.
As for deleting the files, the DMCA doesn't require that. It says:
"(iii) upon obtaining such knowledge or awareness, acts expeditiously to remove, or disable access to, the material;"
Removing the link in question would disable access to the material, which is what MegaUpload did.