[Captain Bunny]

Two tips you might want to try,

1st, before you start the mission, get the fastest car available to you, and one you are comfortable with driving.
Park it outside the Malibu and then go into the club. before you race, jump out of the car you get and into the fast one youve chosen. this is time consuming though and i never managed it that way.

I beat the guy quite easily though, by driving along side him and forcing him into a building so he hits it head on, and you just scrape along the pavement. This gives you some time to get ahead and he never caught up with me.
As for the cops, a bit of car weaving and a little bit of luck and the mission becomes quite fun.
The thing i didnt understand is by beating him, youve just proven yourself to be a better driver than he is, so why let him be the getaway driver?