Is Star Trek 4 a classic? To fans, it's a divisive one. In my older years I'm more inclined to just enjoy it for what it is, situating it within the exhausting three film cycle which it concluded. Bits of it have certainly entered into the greater cultural zeitgeist. I mean, "Hello, Computer" while speaking into the mouse is still a great gag.
The film isn't trying to be great cinema, nor is it trying to be "serious" Star Trek.