I can be a little more forthcoming than this with the benefit of a night's sleep. :-)
The problem with this question is that the answers are fuzzy. Newton had a lot of features that are everywhere now, but that were not when it was being developed. Of the features that have become widespread, it's not perfectly clear which ones have Newton ancestry, which share common ancestry with Newton, and which are mostly independent but possibly influenced to some degree by Newton.
There were a lot of ideas swirling around in the late 80s and the early 90s, and a lot of smart people trying them out in different ways. Some of Apple's best people worked on Newton, and afterward went on to work in other places, taking with them their intelligence and creativity and things they learned working on Newton. It's hard to be sure what they did later, or who they influenced with those ideas.
Take Javascript, for example. It's pretty similar to Newtonscript in several ways. Is that because Brendan Eich knew about Newtonscript and was influenced? Or is it because Brendan Eich was influenced by some of the same things that influenced Newtonscript's creator, Walter Smith? Things like Scheme and Self, for example, and like the idea of using a syntax chosen to seem friendly to C (or Java) programmers. Someone who knows Brendan Eich could ask him, or Walter might know something about it; he often comments here.
Newton had a bunch of features that were wild in 1992, and aren't as wild now. Features like transparent wireless network roaming, seamless migration of data between ephemeral and persistent storage, a purely gestural interface built on machine learning, and a simple knowledge-based help system. It was almost small enough to fit in a pocket--but not quite. I think that's one of the major things that worked against it in the market: it wasn't small enough for a pocket, and it wasn't big enough to have a nice screen. It was exactly in the awkward middle.
Its handwriting instantly became a joke, but it was actually pretty good. Once it was trained, it was actually very good, but one of the things that we learned from Newton was that very good is not good enough in a consumer product. Every small step away from perfection loses you customers.
(Newton's handwriting recognition was unusually good for me, and for the other Newton engineers, because our handwriting training data was built into the firmware. Any of us could make any Newton look nearly flawless because it already knew us.)
Its recognition system was actually more sophisticated than I've allowed: it was in fact several different kinds of recognizers working in parallel, coordinated by a blackboard system. Its ability to recognize drawn shapes and convert them into vector graphics that you could immediately edit in-place was very cool. The fact that you could have all these different recognizers all working together on what appeared to be a single sheet of "paper", doing the right thing, whether it was converting handwriting, recognizing drawings, or responding to command gestures, all interleaved, was even cooler, and I'm not aware of another system that achieves that seamless kind of feeling even now.
The first time I ever saw a freely-roaming networked device, it was in Newton's Bubb Road building in Cupertino in about 1992. It was a Newton prototype PC board ribbon-cabled to a Macintosh SE that was being wheeled around the building on a cart so that the engineers could watch as it negotiated connections with different networks. We all imagined a world where you could have a computer in your pocket and, wherever you went, it would just always have network connectivity. That was crazy talk in 1992.
Newton probably isn't why we have that now; rather, more likely, Newton was one of the earliest manifestations of a dream that lots and lots of people were dreaming, and that someone was eventually bound to get working. Still; 1992. It was science fiction then.
Okay, our present mobile devices are not as seamless as the Newton team imagined, but we do have network connectivity pretty much everywhere. It's so ubiquitous now that people probably don't think it's a big deal, unless they're old enough to remember when we didn't have it.
Was that because of the Newton project, or it happened independently?