You're sort of jogging my memory here...what bothered me...oh yeah. I remember. I didn't like it when the explanation for all the evil that went on with Cordy and the Beast was birth pains. It's not a plot hole as such, just lame. I don't know what else they could have come up with, but if they'd thought about it long enough, I'm sure they could have.
I can ignore that though, because I just love the way they turned the season on it's head. It gets darker and darker with ever more evil deeds and more dangerous bad guys and then...WHAM! You're faced with a good guy. Totally unexpected and kept Angel from going down the Big Bad route that I'm so happy they avoided throughout (not that it's bad in Buffy, just doesn't fit Angel). I just wish they'd planned it from the start so the inconsistencies weren't there.
Why'd The Beast need to kill W&H and take their power?
Well Jasmine wouldn't have wanted W&H to exist. And if we look at it from evil Cordy's POV instead, that's a strong rival out of the way.
In the end, outside of a couple remarks from the characters, why was he even needed to usher Jasmine into the world?
It's pretty clear this was meant for Cordy's storyline and not Jasmine, but you can explain it away (not in a great way) by saying the blocking out of the sun etc. was just the way things had to be for Jasmine's birth. Just a massive ingredient for a massive spell if you like.
He starts an apocalypse -- which would be completely against Jasmine's modus operandi -- and then hangs around waiting for Angelus to pwn him. WTF.
I think Coredlia had different plans for the Beast and he wasn't done yet. That' why she tried to make Angel work for her when he killed the Beast, she needed someone to do that stuff. For Jasmine...I don't know.
If you really want to complain about the Beast and plotholes, you might want to ask why he'd make a dagger of his own flesh for no apparent reason.
Why was Skip in league with Jasmine?
I don't think there's any hole here. Some people just work for others. I'm sure there were benefits for working with a Power That Is.
As the sole representative of whatever force wanted to evil-fy Cordy -- Jasmine? -- he did a pretty shitty job explaining his actions. OH BOY BILLY WAS A RUSE. Way to drag a previously unrelated episode in just so you can write funny Skip dialogue, writers!
Oh I don't know, I quite liked the way they brought the seasons together and can be used to explain a couple of things we hadn't had explained before. Like just why Cordelia was chosen as a higher power and how Angel returned from hell (not that he said that one, I just like to join the dots).