If you mean by "syntax" basic structures of the language and fundamental rules of how you construct a sentence (like the subject-object-verb order), I'd say nothing has changed. Most languages don't change at the fundamental level in 70 years, or in the lifetime of a person.
That said, which grammatical words and constructions are preferred have changed in some cases, especially in spoken Japanese. Off the top of my head, in negation constructions, ないです is a much more acceptable alternative to ありません than it was, and -ぬ (as in 足らぬ) became less preferred over -ない (as in 足りない). You hear less いかに and いかなる for "how" and "what", more どう/どのように and どんな. I'm sure there are many more examples like these. The old words like these can still be spoken, and maybe part of set phrases in some cases, but they generally add an old-fashioned tone to how you speak. (Not too unlike how "thou" and "thee" may sound in English, I think.)
There is a famous song starting with 兎追いしかの山. This would be 兎を追ったあの山 ("the mountain where I chased after rabbits") in today's Japanese. Children learn this song in school and may misunderstand 追いし as 美味し(い), because the 追いし form of the verb 追う is simply not used any more.