Judging from the descriptions and what I saw in the video, stuff like the spotdodge desync will be back from Melee, and other things like the pivot desync will be brought in from Brawl (although I'm not really sure how they kept brawl desyncs considering how they were almost entirely dependent on abusing the 10-frame buffer).
Nana's AI was vastly improved in Brawl. If they're primarily using Brawl's AI, Nana probably won't randomly run away from you. If you don't desync on your own, the only way to be separated from Nana is for the opponent to hit you.
In Brawl you could resync the climbers by doing three things:
1. SideB while Nana is in range and not already doing another special
2. UpB while Nana is in range and not already doing another special
3. Sit still until Nana returns to idle with you.
I dunno if they kept the awkward teleporting Nana stuff from Brawl but if they did, it still applies obviously (I noticed UpB cancelling Nana's Fair endlag, so this at least is in).
From what I could tell, Nana returned to semi-random throws based on stage position (
https://www.youtube.com/watch?v=vIxskj3UFV0&t=1m15s dthrow > fthrow handoff) but since only one such situation was shown anything is possible, really. Most people can only hope that Nana does indeed throw semi-randomly considering that Wobbling is back, because otherwise you would also have Brawl chaingrabs without tripping (meaning much more options with no random chance of failure).