It is possible to gain a boost of spped whilst driving. To do this, you must drive closely behind another kart for a certain amount of time. Once you have tailed it for long enough, wings of air will appear at each side of your kart and you will drive faster for a few seconds. This technique is supposedly known as the 'butterfly'.

In the Donkey Kong's Jungle Parkway level, you can use a Mushroom or a Star to get up the cliff in the cave not far from the finish line. This can cut seconds off your time.

In the Wario's Stadium level, it is possible to use Mushrooms/Stars at certain points to be able to jump over the walls and onto further sections off the track. Using these can cut minutes off your total time, which can help as this is a long track.

I will submit others I find at a later date, when I find them.

In mario kart 64 during the countdown hold the drive butten and you will shoot forward and automatically be in first