The second problem created by the final scene is the problem of Duke Orsino. The audience has to accept that this man changes his romantic attachment in an instant from Olivia to Viola. The audience also needs to be happy for Viola and not think, however secretly, "Man, that girl is a getting a bum deal."
The third problem is caused by Malvolio. There's an almost sickening cruelty underlying the treatment of Malvolio. If it goes too far, the ending isn't happy or even satisfactory, just faintly disturbing.
I have seen three productions so far: the 1988 production directed by Kenneth Branagh; the Complete Works of William Shakespeare version (with Felicity Kendal as Viola and the wonderful Robert Hardy as Sir Toby Belch); and the Trevor Nunn version starring, amongst many others, Imogen Stubbs, Toby Stephens, Nigel Hawthorne and Ben Kingsley. (I've also read a takeoff: a medieval detective novel, Thirteenth Night, in which the jester gets the girl--Viola--in the end.) Of the three, I prefer the Toby Stephens' version. It solves the three problems as best as anyone can.
First of all, it has one of the most touching reunion scenes I've ever seen. The reunion is also immensely clever (I won't give too much away; you really should see it for yourself). The Branagh version falls down here (very disappointingly). I'm not sure what Branagh was trying to do, but the twins' reunion definitely fits the the "oh, hi, there" model. I got the impression that Branagh was trying to avoid being sentimental and gushy. Well, call me trite romance girl, but the reunion ought to be gushy and sentimental! There must be resolution, pay-off, closure. Otherwise, the whole thing is just an exercise in textual self-indulgence. I demand complete narratives! None of this "but life doesn't have closure" garbage. As I told my English Composition students, "We don't do post-modernism in this class." I don't do it in my viewing either: set-up and pay-off, set-up and pay-off.
The second believable thing about the Toby Stephens' version is Toby Stephens. He is, to put it mildily, a sexy piece of compact masculinity. In the other versions, Orsino is tall, almost stooping, melancholy and extremely self-pitying. You keep wondering what on earth an adventurous, sharp and funny chick like Viola sees in the guy. (Which is why the book married her to the fool.) Toby Stephens, however, plays a tautly wound chap who is normally extremely energetic (and equally witty). He does not so much swoon with love as glower with it, and you get the impression, as one should, that his problem is offended pride, more than an offended heart. He doesn't really care about Olivia; he's just bored and she's available and he thinks she should like him. He does care about his servant Cesario (in fact, Stephens' reaction as Orsino to Cesario's "betrayal" is gripping and indicates what really matters to him); he is overwhelmingly relieved when Cesario turns out to be female.
The treatment of Malvolio still bothers me in Nunn's version. The trick with Malvolio is that he has to be so detestable that the audience's pity for him is transient. He has to be so annoying that the audience wants to see him brought down several pegs. Richard Briers as Malvolio (Branagh's version) accomplishes this better than Nigel Hawthorne's Malvolio; the middle scenes of Branagh's Twelfth Night are absolutely hilarious due to Briers' portrayal of Malvolio. Branagh also has the ability to cut and direct Shakespeare in such a way that meaning is immediately intelligable; I used to think it was just Branagh's acting--his ability to speak Shakespearean dialog so naturally, it sounds modern--but I now think that it is his overall style since the cast of his Twelfth Night does this sort of thing much better than the cast of the other versions. In any case, by the end of Branagh's Twelfth Night, Richard Briers' Malvolio has been brought so low that the audience's sympathy switches to the other side. Nigel Hawthorne does a better job at keeping Malvolio unsympathetic to the end. But just barely.
In any case, I think that modern directors make a mistake when they try to invest too much profundity/angst/sorrow into characters that Shakespeare originally intended to be gulls. I think that Malvolio is supposed to be played over the top right from the beginning. We are never supposed to sympathize with him, despite what Olivia says at the end.
Basically, a lot of Shakespeare was supposed to be the equivalent of Adam Sandler movies. And I say that as someone who detests Adam Sandler movies.