I observed the bug on Firefox/XP. The only reliable way I could reproduce it was to move the mouse slightly so that the letter was briefly selected when I clicked. It might be a case of just moving quickly/selecting. I think it might sometimes happen apart from that, but it's possible that it's the same thing but with deselection happening quickly.
I really should have noted that you can just cut and paste the url of you game and send that to your friends if the emails don't get through.
"Sometimes single-clicking on a square made that square get the next letter typed, sometimes it didn't"
I've never seen this myself - what browser/os?
Thanks again.