Combine the "head on a swivel" tip with the "what if" mind game. You can play this game when you're not the driver, too.

What if car X suddenly changes his mind?
What if that man wants to cross the streets?

Combined with a healthy sense of paranoia, this mind game will increase your ability to read traffic and spot potential dangerous situations BEFORE they materialize.

The rest of the advices concerning YOUR behavior - slow down, use due signaling etc - comes naturally as a result when you've been playing this mind game for a while. The healthy dose of paranoia comes naturally, too..