Back to My Mac works in ML if you do the following:
go to:
1) System Preferences
2) Sharing
3) Make sure Remote Management is checked
4) Under Remote Management click on Computer Settings
5) Check all the boxes (Show Remote..., Anyone may request...., VNC viewers may control.....) and put in a password inside the VNC viewers may control screen with password
6) Leave the computer information boxes empty
7) Click OK
8) Click Options under Remote Management
9) Check all 10 boxes, click 'OK'
This will enable the computer you want to watch to be reached if you previously had access under Lion but lost it under ML.
I think some of the boxes I told you to check may be left unchecked, but since this particular method worked for me flawlessly, I would suggest you do this first, and then tweak later. Now, if you didn't have access previously under Lion, that means some firewall is preventing access and you may have to tweak your router -- these instructions will not help you.
This method works over the internet or locally, and it allows ARD 3 to work properly, thank you very much. I use ARD to manage all the computers in my office, and I was pulling my hair out trying to figure why I lost access after upgrading to ML and why our new iMacs with ML would not allow remote access.
These particular instructions are probably buried somewhere underneath layers and layers of help screens explaining how to enable Back to My Mac, but Apple should have it made simple as it usually does.
Hope this works for you. Good luck and you may now upgrade to ML without fear of losing remote access through Back to My Mac.
