How does Bernoulli’s Principle apply to the cardiovascular system?
Bernoulli's principle can be a little tricky when applied to the cardiovascular system, but it still holds true across the entire system. You mention a good point that the relationship doesn't seem quite right at the aorta or arteries, because of the constant fluctuation of pressure between systolic and diastolic without a significant change in diameter of the vessel. Remember that this is due to the pulsatile flow of blood from the heart, and has nothing to do with Bernoulli's principle. If the flow was constant (i.e. not pulsatile) then the pressure would be constant as the diameter of the vessels is constant. As the diameter of the vessels begins to decrease the velocity would increase to maintain a constant value. 

As you mention, Bernoulli's principle describes how the product of area and velocity of flow must be constant across a system. When the total surface area of the system increases, the pressure decreases as well as flow. It is important to remember that even though the capillaries are so small and individually high resistance (which you would think according to Bernoulli's principle should increase the velocity), you are effectively adding an innumerable number of these very small resistors in parallel (not in series) and the resistance overall (and subsequently pressure + flow) decreases greatly. 

When adding resistance in series the total resistance is additive and it adds up quickly! $$R_{Total} = R_1 + R_2 + R_3$$
While resistance in parallel adds the reciprocal of the resistor, meaning that as more resistors (or capillary pathways) are added the total resistance continues to decrease because of the following relationship: $$\frac{1}{R_{Total}} = \frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}$$

The parallel resistance stuff was difficult for me to grasp when I was a student, because it never seemed to make sense in my mind that the resistance significantly decreased when you added all these small capillaries. One of my physiology professors described it well when he said, "Think of adding resistance in parallel, in the way that capillary beds and other vessels are in the cardiovascular system, like giving the blood another place to go." If the blood has more places that it can go, then it's easier to see why resistance falls so much when you add a bunch of extra places for the blood to flow.