Thanks again to Noam Rathaus for catching this one: Microsoft has released the another post-SP3 hot-fix, but fortunately this one should only affect a few users. If you're using Visio Professional 4.x with Windows NT 4.0 running Service Pack 3, you'll need to run the Double-click hot-fix. It seems that Visio uses a custom event handler to detect double-clicks that is incompatible with SP3. No offense, but I think Visio should have fixed that one.
You can download it at the Microsoft FTP site