It could be a display persistence problem.
I suggest to uninstall the driver, reset display persistence and re-install 2.4b1 driver.
In order to reset display persistence you could try the following procedure:
Delete first global preferences - Running in a Terminal the following commands:
sudo rm -f /Library/Preferences/com.apple.windowserver.plist
sudo rm -f /Library/Preferences/com.apple.windowserver.plist.*
sudo rm -f /Library/Preferences/com.displaylink.plist
sudo rm -f /Library/Preferences/com.displaylink.plist.*
sudo rm -f /Library/Preferences/.GlobalPreferences.plist
sudo rm -f /Library/Preferences/.GlobalPreferences.plist.*
sudo rm -f /private/var/db/.com.apple.iokit.graphics
sudo rm -f /private/var/db/.com.apple.iokit.graphics.*
Then you can delete user preferences. This must be executed for each user (replacing $username with the specific usernames)
sudo rm -f /Users/$username/Library/Preferences/ByHost/com.apple.windowserver.*.plist
sudo rm -f /Users/$username/Library/Preferences/ByHost/com.apple.windowserver.*.plist.*
sudo rm -f /Users/$username/Library/Preferences/.GlobalPreferences.plist
sudo rm -f /Users/$username/Library/Preferences/.GlobalPreferences.plist.*
sudo rm -rf /Users/$username/Library/Preferences/Caches
and if needed you can try resetting NVRAM. Running
sudo nvram -c
Note that some of the files listed may not exist on your machine.
Hope this helps otherwise please use the the log tool :
http://www.displaylink.com/support/ticket.php?id=269
and attach the logs here or send them through
http://www.displaylink.com/support/ask_question.php