All my comments are based on single player, that is where I would like to see expansion.
1. Diplomacy
Don't know why this is not mentioned more. Any game without locked teams is just silly, everyone hates me because I didn't kill x ships in few minutes on the other side of the galaxy and the AI certainly doesn't treat itself the same way. Smooth this out, make it feel more realistic if that's possible or more forgiving. And why does the entire diplomacy system always come down to military action, I'd like to see relationships entirely based on trade and commerce. Perhaps missions by the AI to create x frigates for him and a way to donate them for example. Or even a mission to swap x metal for x crystal could improve faction. Think US or UK/Saudi relationship, US needs Saudi resources while Saudi enjoys US arms. Ideally I'd like to see military and commerce missions both available when they tell me they have a mission for me and completing either appeases their insatiable desire for my help. Of course if the emphasis is taken away from military action another way to cause strife between factions needs to occur such as completing missions with one faction having negative effect on another factions standing.
2. Make base defence guns on a par with Hangers.
Currently it feels like it's only worth building hangers and maybe a repair bay or Vasari phase jump thingy. Guns only get built when you run out of slots. I don't agree that we need to improve the effectiveness of base defence, but a balance of the current options would be nice.
3. Wouldn't it be nice if we could change the left hand interface to do like LRM x 40 rather than 40 little LRM icons? Full complements on a great interface, but would be nice for an option like this.
4. Explosions!
currently the way ships expire isn't nearly as gratuitous and exciting as I hoped it would be

5. Races
Not for 1.3, more likely an expansion but wouldn't it be lovely to have more factions for those big epic games.
6. In 1.3 I'd like to have a clock on the screen so I don't end up going to sleep at 5:30 in the morning with work the next day

7. Last but not least perhaps a 45(?) second cooldown on Phase Jump engines to try and reduce the amount people can just ping pong forces to keep their fleet from taking damage. Shouldn't effect travel too much as traversing Gravity Wells normally takes about this time. This would also conversely mean PJI's are slightly better for people trying to catch Ping Pongers as the increased Phase Jump time is added after the proposed engine cooldown expires.