Here's some general driving information that doesn't fit into the other sections:
On the street levels, there's some ramps that lead up to a sharp corner. You can slow down to make sure you don't go flying into the wall, but if you have the timing down, starting a drift shortly before going into the air will slow you down just enough and have you pointed in the right direction to continue driving. Just remember, it's a small drift with a shallow angle, you'll spin out in the air if you turn sharply.
Be careful using your boost before a jump. It's fun to go fast and far into the air, but make sure the jump has enough space for you to land and continue to drive. Sometimes, like the jump right before the finish line in the first career playroom stage, using the boost will either rocket you into the wall or leave you too close to it to make the next turn without slowing down or stopping. Learn the tracks, know when it's safe to boost without going off-course. This applies to corners as well, though with smart drifts you can take a lot of corners at high speed.
Even if you have the auto-respawn option turned on, manual use of the respawn can help you out a lot sometimes. There are some situations where the game may not respawn as fast as you can, or where a respawn would be useful even though the game doesn't see the need to trigger it itself, so being quick to hit that button can shave your time down. The default binding is Y on the gamepad and R on the keyboard.
If you're starting to spin or tumble, slow down or respawn as soon as possible. Getting stable sooner will hurt you less than the much longer time you spend going slow because you kept gunning it while going out of control.
If you're having trouble getting the Minesweeper achievement, here's how I did it: stay around second or third place and make sure that whenever you run into a mine, you get the guy ahead of you too. Once you get ten mines, which shouldn't take too long, race ahead and keep the lead until the game is over. And of course, this is much easier if you choose an early Evade race in Career.
To get the Steady Driver achievement, hop into Quick Race and choose the Schneider Vyper. It grips the road well and will be fast enough to win the race, but not so fast as to make you slip or lose control often. Drive carefully and you should have this one in the bag.