This solution worked for me with the latest version of Adobe Flash and MacOS 10.5.7 (latest software updates installed). However, I am going to clarify a bit more what I did.
Step 1 - Open Terminal (You can find it under /Applications/Utilities/)
Step 2 - To turn Dashboard off:
Type this into Terminal and press enter:
defaults write com.apple.dashboard mcx-disabled -boolean YES
Step 3 - find the Dock process id:
Type this into Terminal and press enter:
ps -ef | grep 'Dock' | grep -v 'ashboard' | grep -v 'grep'
The SECOND number from the left is the process id for the Dock.
Step 4 - Kill the Dock:
Type this into terminal and press enter (replacing '<processid>' with the number you found above, second from the left):
kill -9 <processid>
Step 5 - Install Flash Player per Adobe's installer
Step 6 - To turn Dashboard on:
Type this into Terminal and press enter:
defaults write com.apple.dashboard mcx-disabled -boolean NO
Step 7 - find the Dock process id:
Type this into Terminal and press enter:
ps -ef | grep 'Dock' | grep -v 'ashboard' | grep -v 'grep'
The SECOND number from the left is the process id for the Dock.
Step 8 - Kill the Dock:
Type this into terminal and press enter (replacing '<processid>' with the number you found above, second from the left):
kill -9 <processid>
Step 9 - Press "F12" or whatever function key brings up Dashboard to assure it is functioning again now.