I'll keep a list going here for whatever people want to add.
1. List primary position player played at during their career. (It's silly to see a guy who won 5 gold gloves in CF listed as a 1B. In the end almost every player ends up a 1B or DH.)
2. Include as a statistic the # of Gold Gloves, Silver Sluggers, Cy Youngs, All-Stars, etc. awards a player has won and if possible # of times nominated for an award and where he finished in voting. (If we're going to use that for judging nominations, might as well help people use it to vote.)
3. Include defensive statistics for position players such as +/- plays, fielding percentage, CS% and cERA for their primary position.