I would like to not have it open a file when the application starts. Ever.

How about an option to choose how the app starts? Something like "Start application with last viewed file open"? True/False toggle should do the trick.

Either of these solutions would resolve this issue for me. Thanks for the quick feedback & great information.

When I scroll through a file it "moves" or "shakes" on the screen. This is actually a common problem with iOS apps (most PDF readers have had this issue at some point). The best example I can give is to open a file, touch the screen and "scroll" left to right. The whole file moves. Now "flick" the screen up or down in a traditional iOS gesture and while you get the proper up/down scrolling the file will also drift either to the left or right (depending on your own natural tendancy to flick up-left/up-right/down-left/down-right). The "flick" is just a good way to show the problem, it happens even when you a slow careful drag up or down to scroll.

This is less about the the zoom feature it self, but rather a side-effect of having the zoom at all. The only time it is not an issue is when the file is zoomed out such that the entire width fits on the screen (when there are grey "margins" to either side).