I was able to download a "market app" from both AndAppStore and SlideME for ease of browsing/installing apps from the respective sites. They have both worked fine in terms of downloading/installing apps.
I've only tried a few free apps so far (again, cannot recommend Dolphin Browser highly enough!! and if you tweet, Swift Twit) but some of them don't resize to fill the eDGe's screen. As the device becomes more popular, hopefully app creators will either think about resizing or at least mention whether their app scales to the eDGe's screen.