What is it that separates something that looks bad from something that looks good? What is it that determines whether it's ugly or beautiful?

There seems to be no single property or feature of things that makes them look good or bad. Different things will look good or bad for different reasons in different contexts. A sculpture might look good for one reason and a painting for another. A sculpture might look good in the contexts of academia or fine art but bad as an sacred object in a religious context or as an ornament in the contexts of home or office. A scuplture of one period or sub-genre or culture might look for reasons different from those that make the sculpture of another period or sub-genre or culture. In general, however, I'd say this. Looking good or bad will involve (a) the qualities of the object itself (its color, shape, texture, proportions, etc.), (b) the relationship of the object to its immediate environment or setting, © the relationship it has to other objects of its kind, both not and historically; and (d) the context of meanings and criteria that those who are judging the object bring to their assessment of it.

Are aesthetic judgements entirely subjective?

Now, of course to some extent it depends upon how one defines "subjective" and "objective." But tersely, I'd say this: No, there are relatively objective bases to aesthetic judgment in at least two senses. For one thing, the criteria by which we come to make aesthetic judgments are in a significant way shared by members of our cultures, socieites, histories, and traditions. For another, the cognitive faculties and sentimental structures that underwrite aesthetic judgment are shared among large numbers of human beings.