It seems the Game Center really has issues when it comes to updates. I've had it for the past two major updates and have had the same problem.
Despite limiting the download speed to 10 and 5 Mb/s, the download speed seems to stick around 1Mb/s and below. However, I cannot even think of doing anything else that requires an internet connection as the Game Center seems to hoard all of my bandwidth for whatever reason. Further, it seems that even if I just let it do its thing it'll still sputter out and lose connection, requiring me to hit retry every so often so it'll pick up where it left off.
For the 0.6.7 install, the entire thing gave up the ghost when the installation completed and it was in the final checking install step. It would never finish it and it would also lose connection to the news page. At this point restarting my computer fixed the issue and I did not have to reinstall the update or anything. It is still quite inconvenient.
For the smaller incremental updates of the 0.6.6 family of patches, I was perfectly fine. It's the big, major patches that make this thing look silly. I also seem to have a degradation in connection performance when I have it running (like when trying to stream video), but at least I can control that by exiting the program.
I can put up with these downfalls, but this really needs some work.