You have done a fresh installation of Mint 12 Lisa. Have you applied all available updates for "Lisa" as well?
When Lisa was installed here at the end of last year, during the first few weeks I experienced a lot of gnome-shell crashes, too. (It would restart automatically here)
I cannot tell which (automatic) update fixed the problem. Yet, Gnome has not crashed here for the past few months now.
So in case you have not done so, check for available Mint 12 updates and install them all, including the kernel updates. Doing so is not totally unlikely to make the Gnome crashes disappear.
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GNOME Shell 126.96.36.199
Linux unimatrix0 3.0.0-19-generic #33-Ubuntu SMP Thu Apr 19 19:05:57 UTC 2012 i686 i686 i386 GNU/Linux