When I google it, it seems like there are many of these, like "Little Honey" is a Branch Sport of "Pee Wee" oakleaf, etc.

Does anyone have any experiences with "Branch Sports"?

So now I guess I have to be on the lookout for unique flowers on my hyrangeas.

Also, just in general, making cuttings. If I pick cuttings from the branches with the best (largest, fullest, best coloring) flowers, will the resulting bush have the same flowering characteristics?

Thanks for bringing this up. I always wondered what was meant by the term "branch sport". Am I understanding correctly? Are branch sports cultivated from a wayward branch of an existing cultivar? Hmmm...that might explain why some folks have written about having lacecaps and mopheads on the same plant and why some of my mopheads will have smooth sepals and others on the same plant will have serrated edges on the sepals. I also have some hydrangeas with very different leaf shapes on the same plant. Let me get this straight....if I cultivate a branch that has the more jagged edged leaves, or a branch that has the serrated sepals, the resulting plant will have all jagged edged leaves or have entirely serrated sepals?....Very interesting topic. Maybe one of the hortipros will weigh in......yg