QuickTime player might not be able to play some videos if it doesn't have all the correct CODEC plug-ins. Thus I would recommend getting either VLC - (click on link) __ (choose nearest mirror site) or MPlayer or XinePlayer
And/or get the QuickTime plug-ins; see QuickTime Plug-ins & MIME settings (click on link)

Go to your LW Library window, select Saved Files folder & press the Explore button. Sample image here: Using Library Explore button to access downld folder (click on link) & drag & drop the file onto QuickTime or VLC, etc. in the Dock.