The following actually works in terms of allowing an install of the 3.1.1 update for Aperture, where the update is downloaded from Aperture support.
- Open the Applications folder.
- Drag the Aperture application to the Trash.
- Open the Utilities folder within the Applications folder.
- Open the Terminal application.
- On the command line, type the below command (which is case-sensitive) and then press Return: (or copy and paste)
sudo pkgutil --forget com.apple.pkg.Aperture - When prompted, enter your user password and press Return.
- Insert your Aperture disc and install Aperture.
Then run the update installer package,
http://support.apple.com/kb/HT3805
Have yet to find a solution for Aperture crashing on opening…..have done everything possible.
Art + Photography 
this worked for me:
open up terminal and type:
/Applications/Aperture.app/Contents/MacOS/Aperture; exit
For some reason this works. Opening it through Aperture icon or by clicking on library crashes it..
I have seen some page where they were getting back some framework errors. This isn’t happening for me.. Good luck!