Blur showing up after rendering

You've discovered Vegas's automatic deinterlacing. For high-motion subjects, try setting your project's deinterlace method to "interpolate" instead of the default "blend". This gives a small reduction in vertical resolution but avoids the ghosting you are seeing.

In addition, if you simply stretch a video event to slow it down, Vegas has to make up extra frames somehow, and by default is uses the same blend method to resample the source frames. Try disabling "resample" by right-clicking on the video event on the timeline, then select Switches -> Disable Resample.

This will not give smooth slow motion - you need separate motion interpolation effects such as Twixtor or some trickery with frame rates and intermediate renders to get better slo-mo. The best way of course is to use a special camera with a very high frame rate.