When Greg is racing Jack back home to hide the "fake" cat, they start and stop at many lights. The plastic surgeon let's Greg drive and informs him that it's a brand-new car. When Greg is going fast and hits the breaks, the tires screech and there's smoke. A new car has anti-lock breaks, so the screech wouldn't happen.
It's not a slip up, It makes the scene more exciting to have tires screeching.
And I was wondering how they could lock the wheels up on the car if it did have ABS. Obviously this car didn't, or do you think the tire smoke was an added special effect.
ABS works when you brake hard, what you're referring to is "Traction Control" which limits wheel spin when you accelerate. Please also remember that it's only a film and will probably bear no resemblance to real life. It's fantasy and escapist and just purely entertainment.