First of all, I evaluate for strength and vigor. It doesn't matter how nice a flower is if the plant is weak. I will then grow it on, let it settle in and evaluate the blossom. My criteria, and everyone's is different, is how the flower looks as a clump and from a distance, are the petals evenly formed or are some distorted, are there green blotches on an otherwise nicely colored flower and whether the fading flowers still look pleasing or if they look like they should be chopped off because they make the rest of it look bad.
Doing this I have found that some that I currently own won't make the grade. They bug me every time i walk by so there is no point in keeping them in a focal area. I'll either move them into the hinterlands to naturalize or I'll find them new homes with someone who can love them for what they are.

I hope that others respond to your question, since I wonder the same thing. I have enough plants to appreciate which are the more vigorous, but I still ponder some of the blooms. I think a lot is subjective,and since I am not entering mine in shows it really comes down to personal taste. I have some that I like because they face outwards and really show off their "inner selves", others I adore because they are nearly black. Some people want a star shap and pointed sepals, while othes want a nice rounded cup like shape. Anenomes, doubles, and picotees all have their charms and most of them are keepers for me. What I really waver on is color patterns. I've had a couple I really didn't care for, but then friends comment how lovely they are. I have a few people coming over tomorrow for a luncheon and hellebore tour, and I am really curious about how they will react to some of the new blooms.

I agree that it depends on personal taste if the hellebores aren't being grown for sale. I tend to love green ones --that's how this obsession started, and prefer flowers with no spotting, but once they're in my garden they're like pets. I couldn't "kick any to the curb", smile. Moving hellebores to the hinterlands or giving them away (to a good home, of course) is what I'll do if any of my seedlings are too ugly to bear. --Hard as that is to imagine.

Still, it was very interesting to read what other gardeners look for. I had never really thought about it and now have criteria by which to judge them.