You’re worried about your new lens. You did the tests I recommended here, and things don’t look so good.
First off, don’t immediately pack up the lens and send it back. It may come to that, but there are a few questions you should ask yourself and there’s a bit more work that you should do to answer them.
Is it bad enough to be noticeable in my photography? This is a sensitive test, and is quite capable of finding discrepancies in behavior on opposite sides of the image that will have virtually no effect on real-world photography (assuming that you are not selling images of test charts). If this is the first time you’ve used this test, pick a lens that you’ve had for a long time and have found to be good for the kind of work you do. Test that lens. That will give you an idea of how to interpret the results of this testing. If the lens you just bought is a zoom; test a good zoom you have; although it happens sometimes, you can’t really expect a zoom to do as well as a prime lens in a test like this.
Is it a tilt issue? If there are marked differences in opposite pairs of images there are three possibilities: a) your lens exhibits field tilt, b) your camera sensor is not parallel to your camera’s lens mount, or c) something else is wrong.
Is it a field flatness issue? If all the corners are mushy, and they all exhibit about the same softness, you may have field curvature. If you do, sending the lens back and getting a new one will probably not solve your problem, since symmetric field curvature is likely designed into (or out of) the lens.
Tracking down field tilt and field curvature requires the same additional testing. Redo the test, but this time make four sets of images, focusing in turn on each corner instead of focusing with the target centered. Then do that again, as a test for de-focused images.
Are any of the corners significantly sharper than they were when you focused in the middle? If the answer is yes, then you’ve got either a tilt or a field flatness problem (or possibly both). If they are all sharper, and they are about equally sharp on the opposite corner of each set, then you have focus curvature. You may have to learn to live with it, since it is unlikely that another copy of the same lens will be any better. If all the corners that you focused on are sharper, but the opposite corners are worse, then you have a tilt issue.
If you’re seeing tilt, then you want to find out if it’s coming from your lens or your camera (in fact, it is probably coming from both places at least in part, but we want to figure out which is the most important). In any tolerance situation, there is a tendency to blame the last thing changed for the problem when in reality, the issue is caused by an aggregation of similar-direction errors. No camera has a lens mount that is perfectly aligned. Alignment can shift over time and with handling. Imagine that your camera’s lens mount is misaligned to a degree that a perfectly-aligned lens will look OK. Now imagine what happens with you install a lens with an alignment error that offsets the one in your lens. It still looks OK (in fact, it’s better, but the visibility of the alignment issue is lost in the noise created by lens aberrations and other blur sources. Now imagine that you get a lens that has the same error magnitude of the first lens but in the opposite direction. Now it’s going to look tilted when you test it because the errors add rather than subtract.
To sort this out, take several of your old lenses, preferably ones that are as fast or faster than the lens you’re testing, and of similar focal length. Test them. Do they look good? Then it’s probably your new lens that’s tilted, and you’ll want to send it back. If your old lenses look tilted, and if the tilt seems to be in the same direction (top/bottom, right/left), then it’s probably your camera that’s tilted. It could be your lens mount, or it could be the sensor itself. It makes so little difference that it’s not worth worrying about. In either case, you’ll have to send it to be serviced. If the people servicing the camera find it easier to shim the lens mount than the sensor, that’s what they’ll do. If the reverse is true, then they’ll shim the sensor.
It’s something else. If you can’t make the corners sharp by focusing there, then your lens has poor off-axis resolution. If all the corners are equally soft, then you probably – but not certainly – have a good copy of an indifferent lens. Go back and ask yourself if it’s good enough for what you want to do with it; some perfectly serviceable lenses have soft corners.
If some corners are sharpish and others not, even when you focus there, you probably have a bad copy. Send it back, with a note describing what you found.