In most cases this appears to be a problem with a damaged file or funky filename on the Desktop. I have had several cases of the flashing/ blinking Finder on multiple machines, all down to that, but ONLY on OSX 10.4.3.
Remedy is a tad cumbersome: either boot up in single-user mode and cd to /Users/username*/Desktop or if you have a separate admin account on the machine, use terminal from that one instead. You need to have the root account enabled in order to access a user's desktop folder. Open a terminal window, type 'su' and the root password, then cd /Users/username*/Desktop and ls -l to see the files. In most cases it will be easy to spot the offending file. It typically looks like Blu??_Sky.jpg or something, simply do an rm Blu* to kill it (providing you haven't got other files starting with Blu).
*replace username* with your actual account name
Again, this only seems to be a problem with Tiger. Not seen in Panther at all. Also all files were attachments and pulled from Mail directly onto the desktop.
Good luck!
L.W.