Both Trek II and III have a decidedly TV-movie feel to them. Khan did try to be a bit more epic and cinematic, but at times the lighting in both has that flat TV-series sort of vibe going.
That look can probably be explained by the fact that Star Trek II: The Wrath of Khan
was produced under the auspices of the Paramount TV Division. This was almost certainly a cost-saving measure.
The entire Trek film franchise is one of attempting to be a bargain-basement blockbuster. Outside of TMP, the gamble that started it all, the success of these films was never assumed. The studios didn't greenlight what I would consider to be a blockbuster budget for any of them after TMP until Nemesis, which backfired, and then the 2009 film, which paid off.
Even Star Trek: Nemesis
had a mid-range budget at $60 million, just $2 million more than the previous film in the series (although more than that probably ended up on screen, since Stewart and Spiner apparently accepted salary cuts).