Cops
When playing 1 on 1 against the computer in the last race of career mode (1 per each class), Cops do appear. This is the only level that they will appear. Also, when going by a cop, ethier by going 50 mph or less (until you reach about 5 to 6 car lengths ahead of the cop you will be safe to pick up speed.)But when you fly by the cop, you will receive 5 Stars. After the cop taps you, you will receive a 1/2 star lost. Then after all 5 stars are lost, your busted, and have to restart the level. But if you do get succesfully bye them, and the cop radio speaks that you've gotten away, you will face the cop again most likely if race is 2-3 laps long. (at least) The Cop will reapear about 1 1/4 laps later mattering on the spot. Also, sometimes the cop symbol at the top may also disappear (w/o no cop radio voice about getting away). About 95% of the time after that, you will find another cop very soon.
Never lose a race
When losing a race or getting into to a wreck, press Start. Select "Restart Race" and the race will begin again, not be count against you.