Linden Lab has released a new viewer (V3) that is capable of handling the new Mesh objects, as well as having other new features (like increasing the maximum size of rezzed prims from 10 meters to 64 meters. Editable megaprims, yay!) But, like most new features LL releases, the new viewer isn't working all that great for everyone.
A number of problems have been reported and verified in the JIRA bug tracking system. Both LL and the third party viewer developers are working hard to squash the bugs, but if you are experiencing them now, that isn't much consolation.
I have two suggestions. First, when you install the new viewer, don't just Run the file from the download site. Use Save As instead, then install the downloaded file to a different directory than your current SL viewer. Make sure that you have a desktop shortcut to both the old and the new viewer.
Second, if your frame rate has fallen off a cliff with the new viewer, go to Me/Preferences (CTRL+P). Click the Graphics tab, click Advanced (if the window isn't fully expanded already), click Hardware, and set the Anti-Aliasing to a lower value than the default value of 8. None, 2, or 4 should work fine. (In older viewers, AA defaulted to None, if that gives you an idea of what to expect).
For users of Phoenix/Firestorm, a new mesh-enabled beta version of Firestorm is available. The developers admit it's buggier than they would like, due to a fair number of problems "inherited" from the LL Viewer 3 code. However, it's working pretty well for me.