Near as I can figure, William’s mother was a widow, which would mean that William was the legal owner of the house- up until the twentieth century, a woman couldn’t own property unless she didn’t have any male heirs. Anything she owned was the property of her husband, and when he died, it would become the property of her son. So, if the house was William’s, he wouldn’t need an invitaion.
Also, did anyone catch Anya’s complaining about Spike getting a pass, and showing no remorse about the killings she committed? Apparently the undoing of the spider-demon spell at the end of “Selfless” was the result of momentary regret, not true, deep-felt remorse, opening teaser aside. So much for any potential Anya redemption arc. Not that it’s too late in the season for that or anything. Hell, there’s five more whole episodes left…
Also, I think the reason that the “cure” didn’t work at the beginning of the episode was that Giles allowed the thing to be a public event. Wood was there, and Spike doesn’t trust Wood at all. And, even though Xander is starting to warm to Spike, there’s still a lot of tension there, too. And Giles’s own relationship with Spike has always been strained. Did he really expect that Spike would be able to do the necessary self-examination for the de-triggering surrounded by people he doesn’t trust? He should have just explained what the bit of rubble was for, then cleared the room, except for Willow and Buffy, gotten the hell out himself, and let the spell do its work.
The whole situation left me with the sense that Giles went and scoured the globe for the bit of rubble as a show to hide his true intentions toward Spike. With the chip gone, Giles obviously doesn’t think the soul is enough to restrain Spike from hurting people.
Also, I think the whole song and dance about a general having to make hard choices was blowing smoke up Buffy’s ass. He obviously didn’t intend to let her make the “hard decision” when it came to Spike. Instead, he went behind her back, then told her in a round-about way when he thought enough time had lapsed that the deed would be done before she could do anything to stop it.