I had some problems installing Final Cut Express 4.0 on OS 10.4.11 on a Mac Pro, but I eventually got it running. I didn't find any tips here, so I thought I'd log it. Here are some tips:
1) log into a Admin user ID before installing.
2) after you install it, run Software Update from the System Preference pane to get updates on various things related to Final Cut (there were updates for plug-ins and Final Cut)
3) run "Repair Permissions" from /Applications/Utilities/Disk Utility
4) After running once, I realized that my capture wasn't working because I didn't have rights to the folder that I chose as a scratch directory. I fixed the rights from the command line( sudo chmod ug=rwx /D/FCE), then I went to ~/Library/Preferences/Final Cut Express User Data and delete the three option files.
5) have your camera ready to connect to your computer for the first time you run Final Cut -- it will be used to set some options.
The tips above worked for me, although it seemed to crash--I'm still testing. There are other requirements related to the type of graphics card.
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