This assumes, of course, that the Duke of Gloucester dies as well. If we backtrack by a year or two, we could have that he doesn't. That get rid of that whole rigmarole.
Yeah, he could quite possibly survive, and Anne could live longer as well. Anne, however I don't see living much longer, if we give William almost two decades more to live. If Gloucester survives, he definately won't remarry. I suspect that's why he didn't remarry IOTL -- Anne was alive and well, as was her son. There was no need to 'secure' the succession so to speak. If Gloucester dies though, we can see William remarry not long after that. So anywhere from 1702 to 1714 William could reasonably remarry. Any good potential spouses? Probably from a minor German state, or even Scandinavia seems a good possibility. Butterflies may keep Charles XII alive and well --
Ulrika Eleonora, Queen of England, France, Scotland, and Ireland anyone?
If Anne and her children die, the children of William III will be the legal successor.
About the Dutch, I suspect that with the influence of Willem III they will appoint his son as stadholder (of most of the provinces). Usually only in a powervacuum they succeeded in getting rid of the stadholder (like when Willem II died and his son Willem III wasn't born yet or when Willem III didn't leave any sucessors behind. Although i must admit that the Dutch won't be happy with it and after William's son died they might appoint a stadholder who isn't king of England (possibly the second son or the Frisian stadholder). Noe that i think about it, it might be interesting if Holland (and Zeeland and Utrecht who usually follow Holland's example) would get rid the English stadholders, while Overijssel and Gelderland remain in personal union with England.
A continuing Anglo-Dutch union (for a little while, at least) is quite interesting. I agree, it is probably temporary and after two generations, England and the Netherlands go their separate ways, England for one of his grandsons, and the Netherlands for another. I can see them remaining fairly close however, despite this. It may help the Dutch decline of the 18th century if they are close to the British, perhaps maintaining many territories they lost!
Would an Act of Union or something similar still happen in TTL? I'm leaning towards no, as William has Stuart blood in his veins as a grandson of Charles I, and would be a valid successor in Scotland. Especially if he remarries and has children it seems less of an issue.
There's also the interest of the relationship with France... they went into the crapper as William III was a virulent francophobe. How does he handle the rest of War of the Spanish Successions? Do the butterflies of his longer life mean the war could turn out differently (perhaps better or even worse) for the French? William used the patriotism of the English to fund his war against France, but as it drags on I could definately see them tiring of it and eager to pull England out of the conflict, whilst William feels he must stick it out until the end, especially with his Dutch subjects.