Q: twittertoday.appex

It's not a "virus". You installed an app that invokes a process known as "TwitterToday". If you don't want it, uninstall it.

Remove the Twitter.app for Mac OS X, probably. 

This is the first reference to that particular item and that error that I can find anywhere, which either means this is a unique system, or there's something really odd installed on this system.

If this is part of the Twitter client for Mac — and that's probable, but not entirely certain — then check with Twitter Support.

Assuming you intentionally use Twitter, refer to its developer for support.

I just received this message too and figured out that the Notification Panel uses twitter today to show trends and highlights from todays tweets. It is not a virus...just allow it access or delete twitter from the panel...

Dear JohhnnyO2,

Which Panel and how? It is bugging me every time I try to start up.

BH

The notification page (top right corner button) - click on the today tab (as opposed to the notification one) I allowed the app access and haven't seen the message since. The other option is to delete it

Thanks. Deleted Twitter App and seems to have solved the problem.