Dealing with incidents when you're off duty can be very different from working in uniform. Before you involve yourself in an off-duty incident, it is imperative that you have a game plan in place. As my former boss, Al Materasso (now NYPD's Chief of Manhattan Detectives), often told us, "Failure to plan is planning to fail."
Think about the types of crimes or situations that are serious enough for you to intervene. What enforcement action does your agency (and the law) authorize you to take while off duty? What if you're off duty and outside the jurisdiction where you work (e.g., if you live outside your jurisdiction or are traveling)?
Whenever possible, it is best to avoid disputes by speaking, acting, and driving courteously. I strongly recommend that you read Dale Carnegie's "How to Win Friends and Influence People" and George Thompson's "Verbal Judo" for strategies to avoid entering into altercations.
It is also important to use good judgment about when, where, and how much you drink. If you're involved in an off-duty incident and you've been drinking heavily, you're likely to have a problem with your agency or a legal problem no matter how justified your actions were.
If you're involved in a personal dispute of any kind—with a current or former spouse or significant other, a neighbor, a traffic dispute, etc.—unless you have an immediate need to defend yourself or another innocent person, it's usually wisest to call on-duty officers to respond rather than try to make an arrest or take other enforcement action yourself.