The skies the limit. Let's keep it to purely gameplay features. I will start it off with a few idea of my own. Don't sue me if these aren't new to the franchise or are not completely new.
1. Hanging off the back of tanks or jeeps. What if could go up to a friendly tank and just grab on and hang on the outside of it for a bit? What if you do that with a transport vehicle? That would be fun. Add some excitement. Would have been fun with horses in BF1 too. It would have to work great. And be crisp and polished and no hassle. Maybe just holding down E would do the trick. As long as you held down E you hung on. A big bounce could knock you off. IF the vehicle brushed up against an object it could knock you off.
2. Zip lines and grappling hooks. OK not new. But these were were a blast in Special Forces back in BF2. It may have been in a BF spinoff game too aka Hardline. But this stuff equals fun. Zipping down from the bridge or grappling up to the bridge on Rotterdam for example? How could that not be fun?
3. Jumping from vehicle to vehicle. What if you could jump out of your vehicle and land on top of another vehicle? What if this also could be pulled off in the air between planes? Smells like fun to me.
4. Crawling dead guys. Basically bring the Firestorm feature into the main game. When you're down you can crawl away and even use your pistol to some gimped degree. That might add additional fun.
5. Glider. What if you had some kind of personal glider as a gadget in some class. A wing suit. Something that would let you glide a short distance or drop down from a tall height without damage? Although the zipline is basically the same gameplay idea. So it's probably redundant.
6. randomly generated maps. the idea is the map is never the same each time and thus the experience is always a bit different. The idea is from Diablo which had randomly generated 2d dungeons. Take that and bring to 3d and BF. IT's a complex idea and programming task. There would have to be some limitations. But (it would) be interesting if a few maps were able to reconfigure certain parameters each time so the map would never be quite the same each time it was played. That would help keep the game fresh.