Bring back FP1 + FP2 - With differing objectives throughout the sessions. No idea why they dropped that aspect the last couple of years? (idiots?) I used to revel in the lengthy process of learning a track, figuring out a setup, adjusting for tyre wear, track evolution, weather and trying to conserve engine use over the whole season. If I don't want to play FP1/2 I can just use skip session.
Pit Stops - Player controlled pit stops so there is a chance of a mistake which will cost time. Also not waiting for EVERY car to go past when the pitlane is busy, it is freaking ridiculous how long they wait to release you sometimes.
Pit Stop Practice in FP and Q, - A quick change of tyres and straight back on track. This would also be a chance to hone your player controlled pit stop technique.
More immersion in the career mode - Podiums! Including anthems, and of course, the champaaaaaagne
Bring back (though heavily reworked) the press conferences and paddock interviews. Make the players decisions when answering the press have a direct effect on what teams become either more or less interested in you. Make the questioning more dynamic, I don't want to answer the same questions over and over. Again this was dropped out of the game from previous releases, If developed decently, this could have a huge impact on the career experience.
Warm up lap / Starts - Heating the tyres up to optimum levels could result in a optimum start. Generally, this would make the start more intense and create better immersion. Having a player controlled starting procedure would be cool.
Commentary - What I would give to have Murray Walker commentating on my races! HA! but seriously, bring Crofty and Brundle in and I would be very happy
Engineer - Needs to give more dynamic advice and information during all sessions, not just rinse and repeat. He could have a general knowledge on what kind of setup suits the track/conditions and what kind of runs to do on different tyres/fuel loads. During the races he should not talk you when you are in a wheel to wheel battle or navigating a series of corners unless it is CRITICAL information
AI in wet weather - There needs to be some teams taking gambles/risks. I don't want ALL of the cars coming in on the SAME (ideal) lap to pit for the SAME (ideal) tyres, in real life AT LEAST one team will gamble on the tyres/strategies in changeable conditions.
Safety Car - Though the frequency of it being deployed is debatable season to season, cars that stop on the track, debris on the racing line, extreme wet weather and big accidents should all bring out the SC by default.
Too many times have I seen multi car crashes and the yellow flag is out for not even a lap, by the time I get around to the crash site there is no debris/wreckage just nothing, wouldn't even know there was an accident 90 seconds ago!
Also, the AI needs to take advantage of pitstops during the safety car period, at the moment it seems that all teams will pit on pre destined strategies, this needs a more dynamic approach, again at least one team will be gambling and more often than not it is just common sense.
Release a complete game - Every year there seems to be a major game-breaking bug on release. Surely beta-testing would have found these along with most other bugs pretty quickly. Patches, fixes, and workarounds suck. I'd rather them be focusing on quality DLC throughout the yearly cycle of the releases.