Hi I am having the same issue
I recently installed ARD 3.6 so I could help my parents with their Mac(10.7.4) over the internet.
I am able to observe and control their Mac but I am not able to copy files, install packages, run reports, send messages...
They have a linksys router and the ports 3283 and 5900 are open, TCP and UDP.
I also opened port 22 and 20 TCP (I read it on one site, and saw the list on the Apple site)
I am logging in to her Mac with her Admin user-name, and I checked under preference/sharing Remote Login, Remote Management, Remote Apple events and her user is selected as well.
I ran the Adminstration Settings Report on my Mac(10.8) and the settings are Off for running reports....
It looks like I have to change some settings on my configuration, but I am not sure how to do it exaclty.
Any ideas?
Thanks
LA