I've just updated to Reader X on my Windows 7 Ultimate 64-bit system, on which I also am testing Firefox 4 beta 7.
When reading a PDF document embedded in a webpage, and when switching focus from that browser window to another window and then back again, Reader X behaves correctly in IE 8, but requires an extra mouse click to re-enable keyboard navigation within the embedded Reader X in Firefox 4beta7.
Specifically, if I open an embedded PDF in a webpage in a browser window, then switch to another window (for example, either use Alt+Tab or click on an icon for another open program in the task bar), when I switch back to IE8, keyboard navigation is immediately working. I can Alt+Tab back to the IE8 window and hit Page Up / Page Down to continue scrolling the PDF document in the embedded Reader X.
However, in Firefox 4beta7, upon switching back to the Firefox window, keyboard navigation in the embedded Reader X is not enabled until I click the mouse explicitly within that window. If I've switched back to the Firefox window with Alt+Tab, then I must move the mouse pointer into the Firefox window showing the embedded Reader X and click. If I've clicked directly on the Firefox window, I must still click a second time in the window to re-enable keyboard nagivation in Reader X.
Adobe, please address this in an update, or work with Mozilla if you find that the cause of this unfortunate behavior is something not-quite-right in Firefox 4 beta 7 itself.