|Excuse the blur...|
The trouble is that the change of calendar we have had since Newton's time produced two effects. One is that the date jumps forwards (10 days at his birth, 11 by his death), and the second is that the date that the year changed moves from March 25th (don’t ask) to January 1st.
In the dates that would have been used by Newton himself, he was born on Christmas Day 1642 and died on 20 March 1726. (If he had died instead on 25 March, it would have been 1727.) Alternatively, if we decide to impose our present dating system on the past, he was born on 4 January 1643 and died on 31 March 1727. This is upsetting for those who like to make the handing-on-the-baton observation that Newton was born in the same year that Galileo died.
So which dates should we use? In one case, there is no argument. When talking about the anniversary, we have to use modern dating. So if you said on Christmas day 2042 that Newton was born 400 years ago, you would be plain wrong. But for the rest it's a more difficult decision. It somehow feels right to make use of the dates of the time - but then you have a problem with using BC dates. After all, when Archimedes had his twentieth birthday in 267 BC (did ancient Greeks celebrate birthdays?), he was hardly likely to call it 267 BC or to ponder on the fact that Christ was going to be inaccurately dated as being born 267 years in the future.
The other problem with using contemporary dating is that, for instance, when Newton was alive, some of his European friends were already using the Gregorian calendar. So how do you date an event where Newton interacts with someone in France, say? It's a worry.
I suspect, then, that it's probably best to stick to new style dating. So it's 1643-1727. Okay?