Take a story's temperature by studying its tone. Is it hopeful? Cynical? Snarky? Playful?
Aristocratic, Somber, Comic
If you met two scenes of this play on the street, they would be completely different people. One would be all goth, with dark clothes and loads of tats, while the other would be a pretty cheerleader who just stepped out of a Ralph Lauren Polo ad. Yeah, that's how different the tone is from one scene to the next.
We might chalk some of it up to the fact that it was written by two different playwrights (William Shakespeare and John Fletcher), but it might also be due to the fact that there's a lot going on, and it's going on among some pretty different kinds of people.
Somber
There's something kind of subdued about this play. Even in the end, when the most exciting celebration happens (Elizabeth's christening), the focus is on what's to come and not on the big party itself. What gives? Well, the somber tone ensures that we're always thinking about the consequences of everything.
It's not enough to just see Buckingham taken off to the Tower, or to see Henry divorcing Katherine. Shakespeare wants us to dig deep and really contemplate the ramifications of those things from all angles. Keeping things serious reminds us that this play is about serious, life-and-death things that require a lot of intense thought.
Aristocratic
The tone in Henry VIII isn't just somber; it's also very formal. We see a bunch of formal events: a trial, divorce proceedings, a coronation, a christening, and a council meeting. The language itself is pretty formal—we're usually told about what's happening in the court in a pretty removed way. In fact, we're not even allowed to see a lot of what is going down. A lot of the time, the gents have to fill us in, because the events themselves are invite-only.
Henry VIII is about aristocrats, and the tone of the play never lets us forget it. We're always somewhat removed from our cast, watching them from a distance. Guess we're just not good enough for them.
Comic
And then there are the funny scenes. Yeah, they're there, even if they don't feature your typical laugh-out-loud schtick.
Take the Old Lady, for example. She's just hangin' with Anne, when suddenly Anne gets a surprise promotion and wad of cash from the king. Now, Anne has just sworn that she never wants to be queen. What does the Old Lady do? She says, "There was a lady once—'tis an old story— / that would not be a queen" (2.3.109-110).
Now that's funny: it's like when your friend swears up and down that she doesn't have a crush on the quarterback, and then you catch her staring at him one day. You might say, "What was that you were saying about not liking him?" That's exactly what's going down here.
Even in a serious play like this, Shakespeare tosses in a joke every now and a then to keep us on our toes.