I expect you're spot on, Lutyens, other Queens had been accused of adultery and not even divorced, others had been definitely guilty of it and nothing much had happened. Anne was hugely unpopular though, and there were a lot of people trying to get rid of her, primarily Cromwell and of course the Seymours.
I think Alison Weir, when trying to be fair about it says that Anne was tried fairly according to the law of her time. That is: it was treason for the Queen to commit adultery, as it threatened the succession, and it was treason to plot the king's death or even talk about the possibility of it. And although it seems a travesty of justice to us to read that the accused were not given the precise details of the case against them in order so they could prepare a proper defence (for example being alleged to have committed adultery with X at, say, Greenwich Palace on 1st February when actually on that date Anne was at Windsor and X was at Richmond, but although that can be proved by historians now it couldn't be proved when they were on trial and this was the first they had ever heard of it) - that was what the law was THEN. So Henry wanted her to have a fair trial, and she actually had a fair trial according to the law then and one of the men had "confessed." I do wonder whether if he hadn't said what he said history would have been different.
Trills It was unprecedented for a Queen to be executed. That a headsman was summoned before the trial indicates that it was assumed to be pretty likely that Anne would be found guilty. Of course, he could have been sent home again. But it was pretty cruel to make Anne think for several days that she was going to be burned at the stake, in order to get her to agree to a divorce in exchange for being beheaded, when it was obviously always the intention that she should be beheaded.
Re the weakened claim to the succession, both of Henry's heirs at that time (Mary and Elizabeth) had weak claims to the succession depending on whose side you took. Henry really needed a son whose paternity and legitimacy was without doubt. Which he would have had if Anne had managed to produce one, as Katherine of Aragon died at the start of that very year.
Also, the claims of adultery made it look as if he was impotent and that Anne was having to take lovers in order to get pregnant to save herself. (I think this is the stance Philippa Gregory's book takes.) This is highly unlikely to be the truth.
Alison Weir wonders if Anne was Rhesus negative, as it was odd that she had one trouble free pregnancy but all her subsequent babies died.