1.
The Road to F1 (more interactive career) - is a truly fantastic idea. It would be more engaging than driving season after season in Formula One. It would be a lot of work on the developers' part and issues with licensing, but it would make it a really and truly epic game. That really is what this game needs. Codemasters already has licensing rights for games like GRID and DIRT. Why not use it in F1?
Indeed like zeradin said, it doesn't have to be absolutely authentic, Codemasters could create their own racing categories specifically for the game, or get only the basic license. For example Formula Ford specs, but the teams does not matter all that much.
2.
Better way to predict tyre wear in a race - I always had problems with adjusting strategy, because it was hard to estimate tyre wear per lap, even after going through practice with simulations of high fuel load and so on.
3.
Free Practice and more engaging Car Development - after a while it isn't really fun to go out, do one lap and have new parts on your car. Simulations in free practice, for example are a solution. Race simulations for power unit developments and Qualifying simulations for strictly performance upgrades. Also, return to a full race weekend, FP1, FP2, FP3 in full.
4.
Pre-season testing - not only to get acquainted with the car, but also to determine the development stage of the car at the beginning of the season. If you skip the testing you start with a weak car, if you do a lot of laps, you have a better car from the start.
5.
Some new tracks - it would be great, to have some more tracks in the game instead of always having only the GP tracks. Just because Nurburgring isn't part of the calendar, it doesn't mean that both Nurburgring and Hockenheimring can't be in the game. Same goes for Buddh International Circuit.
6.
London GP track - as presented by British GP sponsors and McLaren drivers, the track around the center of London. Even though it might not happen, it would be a dream to try to drive it even in a game.
7.
Driver controlled pit stops - I can't see a reason why the player cannot control the car throughout the pit-stop process.
8.
Better radio communication - Sometimes the radio is just plain boring and it nearly never provides needed information. When someone is right behind me I'd like to know exactly where he is, every lap. Also, I'd like to know how my Qualifying lap is going, without looking at the scoreboard and ruining my lap.
9.
Sponsors and customizable helmets - bare helmets look boring, it would be nice to have some sponsors on them, if not the ability to choose, than at least the main sponsors of the team one's driving for, and more customizable helmets. All due respect, but Codemasters are not masters in designing a nice helmet.
10.
Formation lap before the race - leave it to the driver, to warm up the car and get a good start.
11.
The possibility to have more input into management - contribute on deciding the development path.