Supposedly, if one traveled at speeds close to the speed of light your vision would tunnel and things behind you would appear in red-shift at the periphery of your view. The distortion is such that it’s hard to see reality. My question is, given that we are hurtling through space at near the speed of light, is that distorting our view somehow? Are we not seeing things as they really are? Does this effect somehow explain how we look back in time when we look into telescopes?
Is there any non-trivial content to the claim that we are travelling at close to the speed of light? Everything is travelling at close to the speed of light… from the appropriate frame of reference.
And I could just as well say that we’re perfectly still… from the appropriate frame of reference.
And that we’re moving at precisely 502 MPH… from the appropriate frame of reference.
And so on.
(snip)
There is background radiation in the universe (at about 3K) which actually allows us to determine speed relative to an absolute rest.
However, it is a bit difficult to determine what percentage of the speed of light (from that “absolute rest” reference point) a particular person means. It is generally when time is considered to run significantly slower than from the vacuum-rest point, but defining what is significant would depend on the observer.
After saying that, I have generally heard it used to mean greater than 0.75c.
Ok, you can isolate the reference frame induced by this background radiation. But does anything special happen in terms of the laws of motion concerning rest with respect to this frame as opposed to another one?
Yes. You don’t create waves in the aether. Duh!! 
My theoretical physics chops are pretty rusty, but I’m pretty sure this one actually isn’t as funny as it used to be. The “aether” is kind of back, isn’t it? Am I right, all you better-informed-than-me physics folks?
The effects the OP is referring to depend on your speed relative to the scenery you’re looking at. The cosmic microwave background is a perfectly valid set of scenery to use as a reference, but there’s nothing inherently more special about it than any other bit of scenery-- It’s just a really big scene, is all.
There are very few things we’re moving close to the speed of light relative to, though: Our speed relative to the CMB, for instance, is only about a tenth of a percent of the speed of light. So that’s why we don’t notice any of these effects.
The short answer is no. The longer answer is also no, but an accident of history and terminology might make it appear otherwise. Back in classical times, “ether” referred to the hypothetical substance celestial bodies were composed of, and was sometimes also called “quintessence”, meaning “fifth element” (no, not Milla Jovavich). Much later than classical times, the term “ether” was re-used to mean the hypothetical medium which supported light waves, but that’s now completely discredited. Meanwhile, the term “quintessence” is now being used to refer to a completely different hypothetical substance which pervades the Universe, specifically one of the possible types of the dark energy that’s apparently causing the cosmic expansion to accelerate. But the structure of dark energy is such that it inherently lacks any reference frame, and quintessence (in the modern sense) has no actual relation to the luminiferous æther that was discredited a century ago.