Definitely worth changing the intake boot & the switch for the brake pedal. The DME showed up loads of occurances of the brake switch plausibility error.
Error 240, Burning Fail showed one occurance on cylinder 6, the one you changed the coil on. Remember that's one occurance since last reset.

Discussion on the code here with mention of rough idle at cold start up:

http://www.bimmerforums.com/forum/showthread.php?2061018-M54-cylinder3-misfire-Asking-for-help-advice

Here's a similar "error 328 burning fail" issue on a different cylinder, replacing the coil seemed to solve it:
http://www.bimmerforums.com/forum/showthread.php?2061018-M54-cylinder3-misfire-Asking-for-help-advice



Here's another one with the same "error 328 burning fail", it looks like this was down to a leak on the intake:
http://forum.bmw5.co.uk/topic/84196-error-code-decipheringwhat-actually-is-the-fault/

Yours definitely needs replacing, it was well cracked, that tape on it is not air tight. We know that needs to be changed anyway, so that's what I'd change next.