Also experience the odd difficulty due to Americanisms, but can't really fault a puzzle coming from something called the New York Times for that. I do however think the puzzle setting for Connections is inferior to The Wall from Only Connect, where they got the idea from. If you haven't seen that yet it's definitely worth a watch (it gets harder as as a season progresses).
I cancelled my subscription a few years back due to the way NYT was covering the current administration. At the time, I believed they'd never offer a "puzzles only" subscription because then they'd lose a large part of their subs. But, I was wrong. And now they offer a puzzle-only subscription.
There's a great documentary about the Crossword with Will Shortz that came out about a decade ago that's interesting.
Spelling bee is also pretty consistent.
I've always thought that Will Shortz was one of the most powerful people at the NYT (slightly joking, but sorta not).
And if you didn't know this, Thursdays and Saturdays can have rebuses.