Confirmed this using mobile safari, like so:

1. In a group conversation (though will undoubtedly work for individual too), write your message.
2. Using the OS keyboard (i.e. NOT the send message icon in the page), hit 'Enter' a bunch of times.
3. Sit back and watch the messages roll in.

The web 'send' icon is disabled on click and during a send, but it seems the 'Enter' action behaves in a different manner, and won't clear the message text, resulting in lots of the same message. I'm still not sure how this occurs (the exact sequence of js calls, etc), so more testing is needed. This might happen a bit, as the latency leads people to wonder if their message is sending at which point they hit enter again and again.