DUI cases are in part based on the reason that an officer had for puling you off the road for a traffic stop. As part of the proceedings, they need to have had justification for the stop and in many cases where a conviction occurs, this is linked to being drunk. Weaving erratically in and out of your driving lane is a good reason for an officer to pull you over. The more erratic you are, the greater a danger you are to other drivers and pedestrians. Driving too slowly or too fast is another reason for the officer to stop you.
In many cases the impaired judgment cause by excessive alcohol intake will result in poor decisions on the road that will draw the attention of the officer like this. In many cases people will drive slow down of fear that they will be caught for drunk driving and end up being caught anyway. Those that drive fast are however often at a higher level of inebriation that dulls their senses making it difficult for them to realize they are going too fast. They may even fly over road bumps and portholes without realizing the damage they are even causing to their vehicles.
Vision problems and slow reaction times also often result in drunk drivers failing to stop for red lights. Running a red light is just cause for an officer to pull you over. Many will also forget basic road etiquette such as signaling when turning or even wearing their seatbelt. Besides the inebriation, an officer will also often pull over a driver for unrelated offenses like broken taillights or damaged bodywork. During the course of your conversation, the police officer may pick upon behavior that suggests you are drunk and request a field sobriety test. Behaving calmly and respectfully can help you in your San Francisco DUI Defense should you be arrested anyway.