It's typical to say that there's no such thing as an "objectively" good piece of art. But if that were so, why would we even bother sharing our thoughts about it? What would be the point in discussing a movie or song or painting with other people if we really thought that all our opinions were ultimately arbitrary? In other words, is there any way to make sense of the way we commonly talk about art that doesn't imply at least some kind of objectivity?

Thank you for your question: a definite puzzle. The real issue may lie in our tendency to divide all our judgements into just two classes, the 'subjective' and the 'objective'. Subjective would be judgements where there is no expectation of agreement from others, and therefore no sense in trying to justify our judgements; so, I like olives and you don't; what seems really pointless would be me trying to convince you that you like olives! Objective concerns those judgements where we believe others should agree with us, because the judgement is saying something about a world that is really out there, and we can all access the evidence concerning the object. So, I say that Jupiter is the largest planet in the solar system and you express scepticism -- well, we can together review the astronomical evidence.
Art judgements seem to be neither one nor the other. They are not subjective, because it does make sense to talk about them, and indeed I may even be able to convince you: suppose, for instance, that I explain the symbolism of a painting to you, and suddenly it makes sense to you, you can see how and why it 'works', where previously it was just a bunch of squiggles. On the other hand, art judgements do not seem to be objective, either, because although we can share evidence there does not seem to be any necessity to your being persuaded, nor any fixed criteria about what evidence might be considered relevant.
We need to invent a category of judgement that is in-between: inter-subjective judgements. The same issue, by the way, arises in moral judgements.

Read another response by Douglas Burnham
Read another response about Art