Here's an insider tip for you. If it's hot, like it was the day I was there, you may want to stick to just one mint julep. Here are the reasons:
First, the mint juleps are all julep with a little mint. In other words, they're almost pure liquor. With the sun and the heat, a few of those will give you a heck of a hangover.
Second, they taste awful! I've had some good mint juleps, but not at the actual Derby. :)
The highlight of the julep is that it comes in a commemorative Derby glass. There are some collectors that have one from each of the years. Note: If you stick around after the Derby, you're likely to find lots of glasses left behind for you to freely take. Just throw them in the dishwasher when you get home - plus, the alcohol will kill the germs. :)