This is a simple workaround in the Spotify Desktop app to remove all the songs that are currently listed in the Next Tracks section of the playlist window. It's a feature users have asked for over the past year and there's still no official way to do it. (This is a workaround posted in Nov. 2015 - future updates to the app might break this function.)
How to delete all tracks from Next Songs section.
This should remove everything from the "Next Tracks" section while leaving your Queued Tracks alone. It should not disrupt playback.
Now you can continue to listen to your Queue without seeing the random Next Tracks that Spotify filled in for you.
*note, the only time I've seen the Next Tracks section even appear after doing this is while an advertisement plays.
*I've only done this on the Windows desktop app (I assume it works on other platforms).