More customization and less restriction, generally.
Example: N7 Shadow. Very fun kit. But I don't like how it was locked to a female human. What if I wanted to be a female Quarian Shadow, or a Drell Shadow? Or the inverse: I love playing a female Quarian, but I don't like any of the female Quarian kits.
This can be solved by making the kits race+gender independant. Each of the 6 classes has a few subkits, like the Inflitrator would have a general purpose sniping kit, a melee shadow kit, and a couple others, and those could be applied to the race+gender of the player's choice.
Another way I'd like to see the kits evolve is for each kit to have 1-2 core abilities (Like Cloak and Shadow strike in the Shadow's case) and 2 more utility powers that are left to the player's choice. In the N7 shadow's example, the kit would always have Tactical Cloak and Shadow Strike, and I could choose to add Overload and Decoy, or Sabotage and Arc Grenade. Or any 2 additional powers from a list of Infiltrator-available powers. This would go a long way to making my character feel like my own instead of a prefab tool that I'm borrowing from someone else.
Armor customization. Like Halo or ME2 and 3's single player. I don't want my Quarians to all look the same. I want my Humans to wear Cerberus style armor instead of Alliance. The ability to choose which faction's emblem is on my gear would be fantastic too! What if I imagine my Human soldier as an elite Cerberus operative or an N7 Veteran? What if I think my Turian Sentinel is a spectre? I should be able to represent that on his gear.
I want to be able to use different melee weapons on my characters. I love the swords that some kits got and I wish I could use one on my human soldier or quarian characters. There should be a new slot for melee weapons on the loadout page so we can decide for ourselves what our characters hit bad guys with.
Also they should do away with the weight system. It made too many weapons have poor damage potential so that they would be light weight. Maybe they could replace it with limited weapon slots. Like every class gets 1 or 2 weapon slots (aside from melee) and they can equip whatever they want in them. Maybe the Soldier class could start with three. Getting more weapon slots could be a potential upgrade to use power points on. I just know that I want a high-damage scoped battle rifle and there wasn't anything really viable to suit that need because all the battle rifles were light weight or in the Adas's case, too slow.
Furthermore, I'd like the ability to equip two weapons of the same type. Sometimes in ME3 I felt like the perfect weapon to carry with my character's Assault rifle was another (different) assault rifle, but I could never carry 2. That made me sad.
More mission types.