I tested a little more, and the worst problem seem to be that in a situation like this:
EDIT: I can't get the formatting to work, but picture a horizontal "HELLO" with "LEMON" coming off the HELLO's second "L".
... and you click on the "l" in lemon, it highlights "hello". You really should NEVER have ambiguity like that. Maybe a second click should alternate between them.
Nevermind, I'm stupid, it does work [the double-clicking].
But lesson learned: Other people are going to be stupid, too.
And apparently my earlier problems were due to latency. If you go too fast, the updates come up a little oddly, and the letters switch 1) When you type, 2) A moment later to something historical, and 3) Back to what you typed.
It's possible the site is overloaded to the extent that ajax messages are getting lost (I have no resend mechanism right now).
Out of interest though, what browser/os are you using?