As per the post Mouse cursor issues, Mass Effect installed just fine through Steam. And it ran very well, too. I understood from the post that the mouse would be entirely undetected, but movement was okay, as evidenced when I set the option Hardware Mouse to YES (with the keyboard). But the mouse clicks were definitely not detected.
I used the diffs linked in that post, applied them to the wine source, compiled wine, placed the winex11.drv and dinput.dll in the Mass Effect/Binaries folder, and voila! Mass Effect is now running near perfectly.
Here are my patched binaries (compiled for amd64 on a fully-updated Xubuntu Karmic box):
I thought about doing a Tips & Tricks about this, because it did take me an hour or so figuring out the little details, but I couldn't see where to create a new Tip & Trick. Am I missing something? Should I bother?
Edit: Oh, I had to click "edit" and then the "add" link appeared. I thought "edit" was for editing the one tip already there :)