The other objects themselves move much, much slower than light. So in general, no, we don't see anything weird. There's no way for one object to be in two places over time such that the light from both places reaches us simultaneously, under normal conditions. You'll always see a single image.

There are some exceptions; gravitational lensing can make two images of one object because the light takes two paths, sometimes offset by time. (A supernova we see from one image of a galaxy can appear in another image of it years later.)

Also, the spirals of galaxies that we see nearly edge-on, like Andromeda, are distorted because the light from the far side is delayed by a few hundred thousand years compared to the front. Not exactly smeared, but, that's getting closer to the speeds and scales you'd need to have.