It goes beyond just some doors -- there's several lines of dialogue in the movie ("Half the doors won't open," "The ship's in pieces"), plus Scotty having just "fixed [that damn thing]" (the Red Alert notification-system), the turbolifts messing up, and the transporters being completely down, which pretty much point to a massive systemic failure of some form aboard the Enterprise
Michael Piller confirmed in at least one web chat that Data's line in that episode was indeed a direct reference to TFF ("Evolution" was the very first TNG episode to air after the theatrical release of Star Trek V
, and it was a nod to that then-recent picture).
Finally, the dialogue dating also confirms that it was TFF that Data was referring to, not TSFS -- "79 years ago" from 2366 is/was 2287, the year after TVH and the launch of Kirk's second Enterprise
(Star Trek III
having taken place in 2285).