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.