I didn't read all the responses, but the attributes I would like to see are:
Day- Night. There is a game I have (something like 24 Hours LeMans) that does this quite well.
Random Mechanical failures. Though not much fun to encounter, I would think this would make the races less predictable. Each race basically has a rabbit, and if you get a car out there with power to stay with or leave the rabbit in the dust, you're gonna end up lapping the rest of the field. That makes some races just an excersise in driving around.
About the field, racing 5 other cars is weak. There are probably limits to what can be simmed, but even 8 or 10 cars would make it more interesting.
I would like to be able to reconfigure the setup (at least the downforce) during pit stops. Envoke more time at the stop, I dont care, but when you realize your tuning isn't exactly what you wanted, you should be able to change some of the settings.
I know you mentioned "other than cars", but there are way too many Honda's, Nissans, etc in the used car garages. I would gladly give these up for another LM car, like a Porsche 935, 956, or 962.
Tacks - add Daytona (with the road coarse) and Sebring. Daytona could double as a stock car track and if you through in a few more ovals, the stock car crowd would be drawn to the game too. I dont care for stock car, but i wouldn't mind if it was there.
It would be cool to be able to build a car too.
Weather. You;ve got ice and snow, but random rain would be really cool.
It would also be cool to be able to manage a team through a season. By that I mean securing a chassis, getting the sponsors, building the car, and dealing with all the stuff duing a race season. Pay to lease a track to test on, parts, a B Spec driver skill, etc, and of course opt to drive it yourself.