Why does the edge of the shadow of a flagpole appear crisp at the base and blurry near the flag.

Hmmm, never noticed that. But here's a guess. Most of the light that casts the shadow at the base comes directly from its source, I presume the sun. But the light striking at the high end of the pole includes more refracted light. It has bounced around more because there are more angles from which light can be bounced before it reaches the top of the pole.

Imagine you had an umbrella stand, and you and two other kids, each with flashlights, stood facing it, with a few feet of space between you. If only one of you shone the light on the object, the edges of the shadow would be crisp. But if all of you shone your lights, each edge of the shadow would be affected by at least two sources, the light from which would overlap, and so the shadow edges would appear less crisp.

I admit I have not performed this experiment, and I'm just predicting the result. If you decide to try it and I'm wrong, I'm sure you'll post and tell us.

Does this make sense to you?

There are a couple of reasons.
The distance from the edge of the flag pole to the ground where the shadow is is less than the distance from the top of the flag pole to the ground. Light refracts the same angle.. but has a longer distance to spread out.
The 2nd reason the base is steady and even a gentle breeze will cause vibrations at the top

Here are a couple more:

The shadow would be more distinct if the sun were a point source. But in fact the sun's diameter extends about 1/2 a degree across, making the shadow's edge a little fuzzy even without diffraction. The increased distance from the top of the flagpole to the ground (pointed out by Peteeo) increases this effect.

I think this is what babthrower was getting at with the flashlight analogy -- light from one side of the sun illuminates the edge of the shadow cast by the other side of the sun.

Another reason is that most flagpoles taper toward the top, and the narrowing increases the above effect still more.

You can appreciate these effects when flying, if you can see the aircraft's shadow out the window. As altitude increases the shadow gets softer and fuzzier until, at some point, it seems to disappear altogether. Seen from the ground, this occurs when the plane is high enough that it subtends and angle less than 1/2 a degree.

By contrast (no pun intended ) if the sun were a point source then the airplane's shadow would always be visible out the window, just looking smaller and smaller as you gained altitude.

Thanks professor. That was my guess exactly. The apparent dia. of the sun. But I wasn't sure.