Completing missions earns you golden whistles. Whistles give you one chance to smash through a police blockade and continue your run each game. In short: complete missions!
Liberating dogs from their owners gives you a bigger doggy footprint as they fan out behind you. The more furry pals you have, the easier it is to collect food and raise your speed.
Use your hard-earned cash to buy new dogs from the kennel on the title screen. Each dog has slightly different abilities - from quicker acceleration to better top speeds. Check them out and you might just find the advantage you need.