One of the other unknowns with using a third-party 'cheapest fare' site is not knowing exactly what fare class of ticket you now own. Many times, these cheap guys are selling what's known as a 'consolidator ticket'...these are tickets purchased in bulk at deep discounts by the consolidator and then re-sold...to consumers like you.
If everything goes fine with your flight, you may never know if you have one of these tickets. But if there is a problem...like a weather delay, your original flight gets canceled, equipment change to a smaller plane...consolidator tickets are usually LAST in line to get help. They also may not be endorsable to other carriers. Lets say you have a Delta ticket and your Delta flight gets cancelled. No problem, you think...looks like other passengers are being re-ticketed to an American Airlines flight that gets them where they need to go around the same time. Except you. Your consolidator ticket only allows for re-ticketing on Delta, so you're left hoping that there is a Delta flight that they can get you on and arrive at your destination reasonably close to your original plans.
