I guess a lot of people say that Henry IV part II is among the weaker of Shakespearean histories, and I can see their point.. It's pretty clearly a sequel, with a lot of the same characters, reprising some of the same devices. There's little by way of dramatic conflict; just a series of something very close to tableaux.
And yet I've liked it from the very first time I saw it some 40 years ago (at the Shakespeare Festival at Stratford, Connecticuct), perhaps the moreso as time goes on. There be more than coincidence at work here: turns out on closer scrutiny that the play has a theme, and the theme is old age, decay, disease (I think I heard somewhere that "disease" is a word first used in this play). Falstaff is a busted flush. The King is on his death bed. Northumberland may have brought about the death of his son. Shallow and Silence present themselves as perhaps the most remarkable old-guy buddy team in literature short of Statler and Waldorf.
It also includes (and I suspect this is most important) three of the most hauntingly wonderful and uniquely Shakespearean prose packages in the canon. One would be that bit where Mistress Quickly tries to berate Falstaff into marriage . ("sitting in my Dolphin-chamber, at the round table, by a sea-coal fire, upon Wednesday in Whitsun-week")The second is the item where Doll Tearsheet suavely beguiles the same Falstaff into blackguarding his great friends while they stand at his elbow (" a' plays at quoits well, and eats conger and fennel, and drinks off candles' ends for flap-dragons). And the third would be that absolutely inimitable "exchange" where Justice Shallow tells old Silence what a carouser he was in his youth (all lies?)("How a good yoke of bullocks at Stamford fair?").
Every time I hear/read Shakespeare do stuff like this, I remember all those people who insist that Shakespeare couldn't possibly have been Shakespeare because he wasn't a college boy. What we have here, of course, are samples of Shakespeare channeling "common speech"--precisely the sort of thing you would not have learned in an Oxbridge common room--and channeling it with a pith and urgency that I think are unmatched anywhere else in literature (no, not Dickens; Dickens stuff is diverting in its way, but it's a cartoon). But wait, no--Shakespeare is not merely "channeling:" he's taking common speech and adding his own particular bite and drive such as to make it all into poetry.
He does it elsewhere, I suppose, depending on your definition. There's a stellar example--perhaps the best--in Act II, scene 1 of Henry IV part 1, the inn-yard at Rochester ("What, ostler! come away and be hanged!"). I suppose you could count the rude mechanicals in Midsummer Night's Dream. although this falls over into more explicit comedy ("The eye of man hath not heard, the ear of man hath not seen..."). I'd count the boost for nationalist solidarity you get from Fluellen in Henry V ("it is out of my prains"). For all this, I don't think any play quite matches Henry IV part 2 in capturing this distinctive mode of expression; all reason enough to keep it among the first rank.
Afterthought: Oh, the play, right, I forgot. I'd say the Ashland troupe did a fine job with it--mostly straightforward and uncluttered. The Doll Tearsheet scenes do seem to get raunchier with the passing years, but I'd say it is all there in the text (guy behind me was loud in his disapproval, though). James Edmondson and Michael J. Hume, whose experience at Ashland extends almost back to the War of Roses, played Shallow and Silence a bit like a pair of vaudeville hoofers (and I say that in a nice way). I thought last year that John Tufts didn't have quite the ambiguity--the combination of charm and menace--that you might want in Prince Hal. I'd say the same now although ironically, he has less to do in this part 2 so you notice it less. Richard Howard, whom I first saw when he strode buck naked across the stage (near 30 years ago, come lammas-eve)--and later, dying in the (literal, Ashland) rain as Richard II--Howard was just about perfectly cast as the ailing and disappointed old king.