Names mostly, the first fal'Cie you encounter is named Anima, seeing as how Anima debuted in FFX, this teams first major FF project, I feel its more than just a re-use of names. There is also a boss named ProudClod which is the name of a boss from FFVII, the FF title most of the team got its start on.

There are tons of references concerning the weapons. I still believe that Nautilus' backgrounds in the dungeon sectioned showcased scenery very reminiscent to the Speed Square ride in Gold Saucer. Your party arrives using a ride tube that is set-up and reminiscent of how your party gets around in the Gold Saucer as well except you can't travel to most of the rides cause people are blocking your way or they are out of order.

I would also like to point out that I find it amusing that Odin controls Lightning magic as he has typically been susceptible to this particular element in past entries.