I've got issues with the Chinese wannabe slayer being used as comedic fodder in 7.
Issues with Dawn/Spike's special big bro/little sis relationship just being dropped in 6. More of a pet peeve.
Issues with Buffy being dressed as a datalounge dude once said, "like a baby hooker". Much preferred her in clothes that looked like she meant business.
Riley the fall guy. I liked Riley but it felt like he was a sacrificial lamb on that show. I don't know if the writers ever meant to keep him around - clearly not - but never felt like he got his due as a character.
Buffy's pointless college career. In 4 she is mocked by a professor for her views. She never struck me as an academic type of gal so it felt very artificial and forced. She drops out anyway.
Giles being pissy and annoying in 7, all of his old warmth and charm gone.
Willow's sudden I'm gay thing. No, she's actually bisexual, but ok. Guess audiences then weren't ready.
I'm sure the article is referencing more cultural things and less subjective ones but that's what I've got for now. Other stuff has already been said or debated and I won't add much that's new.