Depends on what you consider objective. The basic idea of objective quality is that we have set standards of what we consider "good", and things that don't meet those standards are labeled "bad". The problem is that these standards are often arbitrary and up for interpretation when we start applying them to different works.
We can objectively point out plot holes or continuity issues with a story, but other areas of a product such as dialogue, pacing, or even acting are grey areas where large amounts of subjectivity exist. Even some plot holes can be interpreted away by saying "They meant for you to use your imagination", which can actually be a valid argument sometimes. There are a number of different ways to approach any given work, which makes saying "This is objectively bad/good" tricky at best. I've seen quite a few discussions on the quality of a story collapse due to running into situations where it all came back to subjectivity.
However, I don't think there's much wrong with using more extreme examples, such as saying The Room is an objectively bad film (barely a single person would disagree with you on that) or saying that The Shawshank Redemption is a good film. If you take a great film and compare it with a low-budget schlocky direct-to-dvd film, there's just no comparison. There's a certain level of careful craftsmanship, excellence in storytelling, and visual flair that you don't find in "lower" works of art. It's because of that that I'm hesitant to dismiss objectivity entirely, since it's apparent that some works do receive more care and talent than others.
That all said, I just about refuse to engage in a debate about the objective quality of a given work, due to how retarded those discussions often become.
