Flickering shadows may have different causes, but are often related to objects in motion in combination with shadow maps. 
You may experience the same problem if your light is placed at a far distance and your shadow map is too small.  
Turning to raytraced shadows for objects in motion may well solve the problem, but the render time will increase.
 

I'm a Max user and I use it for all my animations (I don't do artwork). But when it comes to landscaping I don't hesitate to turn to Vue 6. Let's face it: Vue produces stunning scenery. I'm in Europe and I frequently use the PAL standard (e.g. 1024x576 if 16:9) for animation. Even with a dual Xeon dual core at that resolution it may take up to half an hour to render one frame from a complex scene. And of course it's all related to my settings. I agree to go for user settings in the first place. But you have to be very careful with supersampling, object and texture anti aliasing.  It depends on your project. A max of 9 subrays/pixel will usually give me a good result (look at your rendered shadows for example), but it may not be good enough for hi quality arwork. Now, supersampling is extremely important in animation, but less important when you create stills. I prefer the way Max handles supersampling and anti aliasing. But if I want to avoid flickering shadows casted by objects in motion, I have to turn to raytraced shadows. And believe me, rendering times will increase sunstantially as well. As far as a Vue is concerned It is always worth it, as others already pointed out here.