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I just got a copy of the Tamron AF 20-40mm F2.7-3.5 SP Aspherical IF for my Sony a7 (using the non-AF Sony A/E adapter) over eBay. I'm seeing what seems to me like a surprising degree of softness from the long end of the lens. This is especially surprising to me since the reviews (see the link) praise the sharpness of this lens. However, I haven't used a wide-angle lens before, much less this specific lens, so I'm not sure whether this degree of softness is to be expected or indicates a problem with the lens. (It was listed as "excellent" condition with no optical problems on eBay.)

All of these shots are uncropped, manually focused, about ~25 feet (~7.5 meters) away from the fence, and handheld because I was too lazy to set up my tripod for three shots. In each case, the sharpest focus was just shy of infinity. (The lens doesn't have focus marks between 10 ft/3 m and infinity.) I took these shots in Raw, loaded them into On1 Photo Raw, and exported them as 90% JPEGs without any editing. Photo Raw doesn't seem to have a profile for this lens, and so doesn't seem to have applied any corrections. (At least, I don't see any differences when I toggle the lens corrections panel off and on.)

First, for reference, here's a shot at 20mm, 1/200 sec, f/10, ISO 160. At 50% zoom I can see some slight differences in sharpness between the center and edges, but that doesn't concern me. I'd consider this shot to have good sharpness for a lens from the mid-'90s.

Next, 40mm, 1/200 sec, f/10, ISO 125. The very center has good sharpness, but everything else is extremely soft, even in the little preview version. The right side is especially bad. This is the problem that I'm trying to understand.

Finally, just in case f/10 might be considered "wide open" on this lens, or there's something about depth of field with wide lenses that I don't know about, I tried the smallest aperture on this lens. 40mm, 1/200 sec, f/32, ISO 1250. I think I can still see more falloff in sharpness towards the edges, compared to the 20mm shot, but it's somewhere between tolerable and good.

This is fairly typical for wide angle zoom lenses, even those that are a lot more expensive than the Tamron AF 20-40mm F2.7-3.5 SP Aspherical IF. Roger Cicala, the founder and chief lens guru at lensrentals.com, did a blog entry regarding this very thing a while back.

Painting Zoom Lenses with a Broad Brush – Roger’s Law of Wide Zoom Relativity

After testing ten copies of each of nine different wide angle lenses in the 15-16-17 mm to 24-28-30-35-40 mm range, he concluded:

At this point, I think, the pattern is pretty clear. For simplicity sake, I think it best we give this pattern a name, and I think the logical name would be “Roger’s Law of Wide Zoom Relativity” since wide zooms are relatively sharper at the wide end. Are there exceptions to this law? Yes, but they are few and far between. For a few of these sets of 9 copies, there’s one lens that’s better at the long end than at the wide end, but for most there are none. No set tested averaged better at the long end than at the wide end.

He then went on to similarly test 10 copies of 8 different standard range zooms (typically 24-70mm or 28-70mm), and said:

Again, you can see the pattern; standard range zooms tend to resolve better at the wider end, not as well at the telephoto end. I didn’t show them, but 24-105mm and 24-120mm zooms have the same pattern. So the Law of Wide Zoom Relativity seems to hold true for zooms that go from wide to slightly telephoto. I can’t tell you if it’s true for superzooms, like 18-270s, because I will never, ever test them. Life is too short to test 10x zooms. I can tell you that it’s not true for 70-200 zooms, but that’s the subject of a future post.

In your specific case, you probably have a copy that varies even more than the average. It's not that unexpected with a lens such as the Tamron AF 20-40mm F2.7-3.5 SP Aspherical IF. Roger has stated elsewhere that many of Tamron's lower cost lenses, as well as those of other lens makers, don't have internal adjustments to correct for differences in manufacturing tolerances like higher end lenses do. With such lenses, what you get is what you get. That's probably why it was sold on eBay shortly after the original owner bought it.

A lot of folks will test new lenses after they purchase them. If the lens performs as well as or better than what most reviews indicate, they'll keep it. If it does worse, they'll sell it and try another copy until they find one they want to keep. There are even a few buyers that will purchase multiple copies of lenses at the same time and test each one. They'll keep the best of the bunch and resell the rest.