Can third-party apps change the color of the... what's it called, Status Bar? If so, why would they want to accept screenshots that cut that out? And if not, why do it at all if the purpose was to make the UI blend?

Status bar changes when a phone call is in progress - Apps can either handle it or the entire app gets pushed down.

I noticed that I can't see the full screenshot anymore on my 4S (need to scroll to see the whole thing) in the new app store app details - a bit annoying.

Screenshots are displayed in the app store. You can include the status bar if that is the way your screen looks (If it's a game or graphic app it will hide the status bar). Screenshots are also displayed when an app is loading. In order to use the full resolution of the iPhone 5 you HAVE to supply the larger png (that is actually how you tell the OS you are supporting that screen size). Neither of these have to be real screenshots by the way. If you read the email it says that you only need to supply the larger screenshot if you are supporting the larger screen - which is pretty obvious, but some developers may not have done so as they are transitioning. There is really nothing going on here.

With iOS 6, the prior solid status bar is now an adaptive color status bar (which is seen in the phone, messages, and other apps). It adopts the very bottom color of the navigation bar (which has to be set using Cocoa Touch elements).

There are a couple of reasons why the adaptive status bar wouldn't be used, both design reasons and program limitations. For example, to be able to use the adaptive bar, the app needs to use the Cocoa Touch UINavigationBar and some apps go about other ways to achieve a similar design without using Apple's native frameworks (like embedding web elements as an app). Then others just prefer the black bar, it allows them to "contain" their apps within the window (e.g., Safari, Notes, or the new Maps app).

In the App Store, I don't think many people notice or care since its a utility to the phone and skinning it is just an adaptive styling outside of function.