How can an app be running yet not appear in the Dock? On two instances, I've been unable to empty my trash because it contained a pdf that the system claimed was in use. On both occasions, I typed the lsof command to find out which app was using it. In both instances, Preview was indicated -- yet it wasn't shown in the Dock! Activity Monitor does show Preview running.

How can this be?
It's possible that the plist of the application has been changed (eg, /Applications/Preview.app/Contents/Info.plist).  There is a setting LSUIElement, which if is true, causes the app to be hidden from the dock, the ⌘-Tab application switcher, etc.  See this similar question for more details.