Yeah the PGR4 intro is god-tier too. FM3's intro was awesome too with many types of racing showcased (and the famous wheelie at the end).
Speaking of intros, I wish we could rewatch FM4's Clarkson one... :-/
Camera shakes are one thing but I think beside that, to achieve realism, Turn 10 also has to work on getting past the video game look. BF3 looks so amazing partly because it has those shits on the camera which go a long way to make you forget that you're a virtual camera in a perfectly clean 3D space. (don't know if I'm very clear on that)
It may seem weird but I believe, Turn 10 has to introduce imperfection to make things more believable.
One example is the cockpit view, the glass should be more or less dirty depending on the the lenght of the race, whether you've been in the grass, etc... It just shouldn't be crystal clear like today.
Glass reflection like in PGR4 (again !

) also need to appear.
It's the same thing for the mirrors, at the moment they look like magical AMOLED screens that stay shiny no matter what...
Some BF3 like stuff on the camera could add a lot too.
Also, bring back dirt on cars with the option to remove it in photo mode (if I had my way, many thing would be switchable in photo mode

).
Get rid of the ugly scratch textures that some car have and make better use of it (if I just rubbed the car against an opponent, it shouldn't magically become all white).
Etc..
So many little things could add a lot...
Although, all that would have to be done after they've nailed realistic colors and look on all tracks, made the massive bloom a thing of the past and added better HDR.