We recently updated to the 2013Q3 production release.
I have found that it is not possible to edit tables using Design mode in Firefox versions 10 through 16. Clicking on the table appears to causes the cursor to jump to a random location and the editor to lose keyboard focus. Typing causes unpredictable results but in several cases Firefox crashed.
Didn't try 17.0, but 17ESR works properly so I'm guessing 17 onward is good.
The problem is reproducible on the Editor demo page.
I submitted a bug which was declined last night. Was told to use DIV's or upgrade Firefox....
I don't know if declined suggestions see the light of day so I thought I'd try to save someone else several hours of investigation.