Congratulations to Mr. Stock for his debut puzzle in the NYT! I've been seeing more and more debuts recently, which is great for fresh blood and ideas.
And in today's puzzle, that shows up as 16 Xs in the grid. The revealer comes at 59A: Words of correction ... or a hint to 16-, 20-, 36- and 54-Across (STRIKETHAT). At first I was confused what that might mean, as I had only one theme answer fully in place, and another where I mistakenly only had 3 Xs in a row. Could this be related to bowling, I wondered? After all, X is the symbol for a strike.
But no, it's more straightfoward, in a sense. Each of the phrases has the string of letters T-H-A-T that have been replaced by Xs. Thus, 16A: Cocktail specification (WIXXXXWIST) is actually "with a twist" while DEAXXXXAFUNERAL is "Death at a Funeral." Nicely, in each phrase, the string crosses multiple words, hiding "that" more effectively.
The theme means that there have to be 16 down answers with an X in it (actually 15, because EXOTOXIN crosses two theme answers). Unfortunately that results in things like LEOXI (although it's cute that the clue recognizes this particular pontiff's historical insignificance), XIS, and XER. But PROXYWAR is very good.
How cute is 38D: More than can be imagined (AZILLION)? Fun clue, fun answer. I also like VITRIOL.
In the end, with such constraints in place, there's not a ton of room for zingy answers and clever clues. So while I like the concept and approve of so many Xs, I didn't love the puzzle as a whole. YMMV.