Lots of really great ideas in this thread, I'm just chiming in with a small list:
Mechanical: More freedom of options for engine bore, stroke, cam, forced induction (per Neema). And like Tenacious said, give us a proper dyno sheet that we can tune our transmissions to.

I want to shy away from a full swap only because a miata with a ford 5.0

in it will no longer behave like a miata.
Interior: Weight reduction should reveal bare metal in the cabin, and rollcages should be present or not, accordingly (zep,

). While I would quite enjoy seats by Recaro, wheels by Momo and the like, I want this game to ship in my lifetime

, so I think generic racing parts will suffice nicely (that is, effected by the weight redu, not at whim).
Exterior: Wheel choice (a la GT4) and paint shop are must haves at this point, a livery editor would be nice, but I don't need it. Body mods should, imo, be limited to functional pieces that contribute to going faster (spoilers/splitters, diffusers, canards, etc.) The last thing we need is 35 pounds of fiberglass hanging off the side of the car, slowing us down.
Race Modification: I would like to see an option for certain cars, either at the manufacturer or tuner or both, that irrevocably modifies the whole chassis and body to that of a full race car (with tuning options changing too).
SOUND: The single most important, visceral, gut-wrenching, feel-it-way-down-in-your-toes quality of a hopped-up track car is the howl of those flaming hydrocarbons as they rip free of their earthly environs. A turbocharged, overbored V6 on the squeeze isn't supposed to sound like my norelco shaver! I guess my point is, I'm willing to forgo a touch of realism in the sound department if they put the roar back in the horsepower.
I think that covers it, until I think of something...
-General