No, they cannot make an objective judgement. To believe they can is to completely misunderstand what the word objective means. They can make a very informed subjective opinion, but the relevance of that opinion is more likely to lie in how much of that experience aligns with yours. Their opinions may be more sophisticated and nuanced in the context of the field of art criticsm, but that's really only relevant to other art critics. I personally find modern art with a colored red box on a white canvas to be a complete and utter joke, but many art critics find such works incredibly interesting - it's not that I'm missing something, or that they're seeing something I'm not. It neither. Art by it's very nature is subjective, since it must be interpreted and receieved by the viewer before it has any meaning. 2 + 2 will always be 4 no matter who is doing the adding. THAT'S objective.
I'm referring to observable properties of the work itself. In terms of painting, you can examine color palette, characteristics of brush stroke, perspective, subject choice, etc., and how deftly the artist employs them. You can separate an analysis of these techniques from a subjective opinion on their result. With your red-box-on-blank-canvas example, one could definitively say that it took less technical skill than a realistic portrait, and have reasons to back that up. This judgment doesn't necessarily inform the emotional impact, underlying meaning, or value of the work in any other context, but is nonetheless a valid observation.
There is certainly the ability for many people reach a consensus of sorts on subjective quality. But it's still a shared opinion. That doesn't take away from it at all, but that doesn't raise it to the level of an objective math problem. It's the fact that many people agree that Rembrandt was a master that makes him one, not the art itself. Different people and generations will come to different conclusions.
I think you're reducing critique to an emotional response, and tangling that up with critical assessment. I'm not talking about looking at a piece of art as a whole and being able to definitively say, "This is good" or "This is bad." But one can say, "This artist employed a realistic use of color and texture," or "This work displays a flawless use of perspective to show depth," and that will always hold measurably true.
Think about it in terms of music. I'm not a musician, but I can appreciate music. I know nothing about music theory, playing an instrument, or any such things. Still, I just feel a certain way about some music, even if I can't explain it in terms of notes and harmony. Should this invalidate my opinion on music? I dont think so, although musicians and critics may find my analysis lacking. But I will likely find theirs as well, as they're referencing things I don't understand or care about.
See above. I feel as though you're making my point. You might have a personal impression of music, but you don't understand it from a technical point of view. An expert or experienced musician would, and therefore has a basis on which to make objective judgments.
Example: Someone with a good ear can identify a challenging melody and explain how a guitarist played it impressively. You might not like how it sounds. These two ideas are not at odds, but if you were to say that the guitarist did not play properly,
you would be demonstrably wrong. Your subjective opinions are equally valid, but an objective critique is available to the expert where it is not to you, even if you don't care.
In terms of LOST, I feel even a non-writer can identify narrative deficiencies and be provably correct. It doesn't take an accomplished author or screenwriter to find some of its plot holes. Can we take those issues and make some judgments about overall quality? I think we can. Can we conclude definitively "LOST sucks" or not? Probably not. How much an individual enjoys the show despite its flaws will always be variable. My point is only that the people who love the show should not deny that those things exist by trying to say the show is immune to this kind of criticism.