The most common mistake people make when thinking about beauty is probably to confuse "pleasure" with "beauty."
You and I both look at a painting. I am pleased by the painting, and say it is beautiful. You are not pleased by it, and deny that it is beautiful. What do we conclude?
Rob would conclude (or perhaps he wouldn't; see his subsequent comments in that thread):
...the inner beauty--the state of the soul/spirit--of the beholder must be projected onto the object-in-the-world, endowing it with beauty, rather than the reverse.
If taken literally, that's absurd. My looking at a painting doesn't change the painting. The only change occurs inside me. But what is there inside me to change? My knowledge (or experience or idea) of the painting.
Now, if you want to say that I think a painting is beautiful because of my own inner beauty, who am I to argue? Even so, the fact would remain that it is the painting I experience as beautiful. There is something about the object-in-the-world that, when apprehended by my mind, I find pleasing.
In Rob's example of a dandelion, we have the color and shape of the dandelion, set perhaps against the uniform background of trimmed green grass, that the admirer finds beautiful. The color and shape of the dandelion exist in the dandelion (or, if you prefer, there is that which exists in the dandelion that produces the sense of color and shape in the observer); these are objective properties, properties of the object-in-the-world. It is the same color and shape that the gardener perceives as ugly.
So while "beauty is in the eye of the beholder" certainly means "beauty is subjective," it's also certainly false. What is subjective is the pleasure beauty causes. But this is an intellectual pleasure, which means that two people can have the same sense experience yet apprehend it differently because they derive different ideas from the sense experience.
Beauty itself exists in the thing sensed, by definition. (And if you don't agree, try defining beauty in a way that doesn't mean the pleasure caused by beauty as I define it.)
As an analogy, think of two people in a forest, both looking in the same direction. The sight causes one person to feel excitement and a degree of anxiety. The other person, who does not realize that that tree stump fifty yards away is actually a large black bear, does not feel any excitement or anxiety. Is the bear projected onto the forest-view-in-the-world by the first viewer?