So, this is entirely opinion based. You might not agree with what I think here, so I ask that people don't comment with abuse simply because I don't give your opinions in my own; constructive debate, absolutely, destructive abuse, leave it at the door please.
Anyway, here we go:
10: No Blue Haired Super Saiyans!
So, first up, and therefore least important; Super Saiyan God Super Saiyan. Super Saiyans are blonde, this blue haired variant A. looks dumb and B. completely breaks what we know about Super Saiyans. Ergo, I hope to see it scrapped in favor of the proper Super Saiyan forms we know and love.
9: Un-Yamcha Gohan.
So, in the new movie, Gohan has been "Yamcha'd"; that is to say, he was pretty competent... And became general cannon fodder. Hell, at the end of DBZ, he was the strongest non-fused fighter, so I hope to see that come back. Among other things, it'd mean Goku and Vegeta weren't the only competent ones around!
8: Make Some Non-Saiyans Relevant Again.
So, by the end of DBZ, it was essentially a case of anyone who wasn't a Super Saiyan sucked. Let's see that changed; I can understand Krillin and Yamcha not measuring up, but Tien was powerful enough he could at least slow down semi-perfect Cell (which always made me question how Krillin was the strongest Human come Buu saga; I smell author favoritism...), and Piccolo was always quite high up there in terms of power, so let's see that back. If nothing else, let's see Piccolo be useful again, he was awesome.
7: No more Super Saiyan Forms.
We don't need any more. We've got 1 - 3, we've got god and we've got the aforementioned awful blue haired one, we don't need any more. And if we get another, give it to Gohan, Goten or Trunks, not Goku or Vegeta.
6: Let Someone Other than Goku be the Hero.
I don't know about the rest of you, but I'm sick of Goku beating all the villains. They haven broken this mold all of once, when it was Gohan. Let's see Gohan be the hero again, or Vegeta, Goten or Trunks. Just not Goku every time. It's become more formula than people saying "Batman wins because Batman" on forums.
5: Don't Push Exisiting Characters to the Background in Favor of Newer Ones.
Looking at GT, my big gripe stemmed from this; Vegeta, Gohan and Goten were all pushed to the background in favor of Pan. Later, the same was done to Trunks as well. TBH, the only character who could use less focus is Goku, since he's now well established, we know the character, give some other characters growth.
4: Let Goten and Trunks Grow Up.
The point is self explanatory. Goten and Trunks can't stay kids forever. Let's see those late teen versions from the end of Z; I'm curious to see how Goten looks as a Super Saiyan then.
3: Let Goten and Trunks be Useful Without Fusion.
Another point for Goten and Trunks; when we had kid Goten and Trunks, they basically became useless unless fused once Gotenks was introduced. Let's see them be able to work well as single entities, with Gotenks as their trump card. This could also help with the whole "let someone other than Goku be the hero" thing.
2: Explore That Part in Battle of Gods.
In Battle of Gods, there's a point where Beerus hits Bulma, and, in his rage, Vegeta briefly becomes more powerful than Goku. Let's see more than that, and see if Vegeta can actually outclass Goku.
1: Give us Some Decent, Original Villains.
The big one; we need villains who are original and don't rely on any established elements. DBZ had this beautiful, almost Shakespearean conflict between good and evil, with villains to that caliber; Vegeta, Frieza, Cell, Buu. Then in the trailer for Super we get a fat Beerus; it feels like they're going along the "fat - thin versions for different powers" route we saw with Buu, and we don't need that. We need a new villain. Hell, even a re-visited older one with new ideas (I'd love to see Raditz and Nappa come back as Super Saiyans, or a new form for Cell) but not a complete re-use of an old trick.
So, that's my lot. Let me know what you think :)