1. The AR and the subsequent S7 (LACK OF) aftermath: It's been done to death on this thread so I won't bring it up again but this more than anything dates the show and makes parts of it unpleasant to watch. Has to be fixed with better, braver and more consistent writing. Don't bring up an issue only to downplay it in such a grotesque manner. Always bring it back to Buffy, its her show and that's why the majority are here.
2. Soul lore: Work out what 'not having a soul means' in human terms (like Billy or the kid psychopath in Angel s1 IGYUMS), in demon terms (do vengeance demons have souls? we find this out very late in the day and it has huge implications for Anya) and for vampires. Angel, Darla and most of all Spike have different reactions to various states of soul-ness that are widely inconsistant. In the end the writers seemed to shrug and claim that Spike was somehow 'special'. What a lazy cop-out that makes his character worse.
3. World Building In General: This would be much more of a problem if we didn't have the Angel spin-off which bolsters a lot of general demon lore, history and how the magic world works in the wider world outside the little town of Sunnydale, but its still really thin. This is the main problem with the Buffy comics which fail completely at world building in any coherent, narrative sense.
4. Slayers in particular: Clear up the lore, the shared slayer dreams, prophecy, the remembering of past lives/deaths, The slayer called before Buffy, potentials and their watchers. The storytelling possibilities are great and varied. Many universes have vampires, explore the thing that makes your world unique.
5. The various clunky plot devices: Acathla, The Initiative brain chip, Angel's gypsy curse, The Key, the cults surrounding the Key, etc. The writers tend to bring something up and then just...hand wave it away because they don't know what to do with it. Part of the writing process is dealing with the story elements you've put in place. It's annoying that they don't do more with or resolve these things.
Other issues:
The First Slayer being black: Question, would it be better if The First Slayer was a beautiful Aryan white woman, the progenitor of the entire line of superior warrior women? Probably not right. Sinaya being of African origin makes perfect sense given the 'since the dawn of time' angle.
As for the hair crack, context matters; you try and murder me and my friends, I get to make fun of your hair because that's what Buffy would do. People should stop playing the victim card all the time.
The Guardian being white: I have a problem with their mere existence never mind anything else (the story narrative always has more value than the meta-narrative), they're kind of a dumb idea to be springing on the audience so late in the game with a 'I'm the last of this secret mythic society' *snap* 'And now I'm dead and irrelevant bye' If they exist make them logically consistent with what has gone before; maybe Native American? that was a spiritual/mystic and somewhat Matriarchal society? how to get more diversity but also avoid various tropes. Hmn.
More black and Hispanic characters: Sure, after all this is California not Kansas. The show should make some effort to reflect actual reality as much as possible, it gives the show more verisimilitude for sure.
Cordelia's Character: Blame S3 Cangel. I really liked Cordelia's development over three seasons of Buffy and 2 of Angel that was crushed by the forced romance and soapy garbage that consumed much of Season 3's subplots. I didn't want Cordelia becoming a bland proto-Buffy and losing her spikey personality just to appeal to dork!Angel. No! *wags finger* No. The subsequent season not only had to undo it they had to explain it away.
Racial Stereotypes: Yeah, this can bug but it goes further than racial into national (Doyle the heavy-drinking Irishman, Wesley the prissy repressed brit) and then just actual stereotypes. The show uses stereotypes all the time as a kind of character shortcut, its not just a race thing so it bugs less only because its consistent.