I'd say the entire race GUI is very barebones. Having all the statistics after race would be nice. You could implement the "medals" in a similar fashion that Battlefield 3 does the post-match results. So you have a results table with kills, deaths, points, ping and then another tab for assignments, awards, class unlocks, and weapon/score statistics.
In GRIP you could have on the results screen best lap time and overall race time along with points and ping if applicable to the mode. Then on the next screen the medal/awards that Broscar mentioned then on the next screen some miscellaneous stats, like amount of drift, percentage values of how much you drove in general and in this race on the ground compared with walls and ceiling. For example you drove 500km in total and 60% were on the ground, 24% on the walls and 16% on the ceiling, while in the race you drove 40km and 76% were on the ground, 10% on the walls and 14% on the ceiling.
Small things like this could really make the stat screen look good. And since there's no pesky open world to bother with, you can create a completely new screen for just the post-race results, instead of looking at the car driving. Would be useful for those that like to give their PC a bit of a rest in-between the races.