AdobePDFViewerNPAPI shows up in Mission Control

I've long experienced this problem, too. Haven't found any 'good' solutions, so put together some Applescripts that partially address the problem. It's very much a kludge and not a perfect solution, and deploying the scripts in a given user's workflow is a matter of individual taste.

Here's code to open an MS Word document in a space that doesn't have any Word windows without first triggering a shift to a space with a Word window open:

tell application "System Events" to tell process "Microsoft Word" to tell menu bar 1 to tell menu bar item 3 to tell menu 1 to click menu item 1 --open
tell application "Microsoft Word" to activate

And this script will close an MS Word document without triggering a switch to another space (if it was the last Word window open in the current space):

--Is there another window of the app in this space? If so, don't need to shift to another app before closing
tell application "System Events" to tell application process "Microsoft Word" to set _theWindows to name of every window as list
set WinNum to number of strings of _theWindows --(Office puts weird other things in the list)
if WinNum = 1 then --i.e., it is the only window in the space
    tell application "System Events" to keystroke tab using command down --switch to another app
    delay 0.1
    tell application "System Events" to set visible of application process "Microsoft Word" to true --in case there is a close dialog I still need to see
    delay 0.1
end if
tell application "System Events" to tell process "Microsoft Word" to tell menu bar 1 to tell menu bar item 3 to tell menu 1 to click menu item "Close" --close

You have a couple of options.

If you move the mouse to the bottom-center of the screen it will appear a menu where you have an option to save to disk. See image below.

Additionally, you use Print option, and there is an option in the bottom-left of that menu called PDF that you can use to save the document.