Sony lenses have a reputation, particularly among the lower priced ones, of fairly sloppy alignment between the various lens elements. Roger Cicala, founder and lens guru at lensrentals.com, refers to it often enough. Such issues will always be compounded with zoom lenses as compared to prime lenses.
The wider the ratio between the shortest and longest focal lengths, the harder it is to make a lens perform optimally throughout the zoom range. Most high quality zoom lenses stick to a ratio of 3X or less, such as 24-70mm or 70-200mm workhorses. If all of the zooming is at telephoto focal lengths, one can stretch that to about 4X, such as with 100-400mm or 150-600mm lenses.
With lenses that start out at very wide angles of view and zoom all the way to telephoto territory, it gets more difficult. Your 18-200mm lens has a greater than 10X zoom ratio and starts out at 18mm. That's a tall order for a lens at any price. To do it and sell such a lens for only $750 makes it that much more difficult.
But it's not just Sony. Zoom lenses in general have a much steeper hill to climb when compared to prime lenses. A minor alignment issue might not be detectable looking at moderate enlargements from a prime lens or from the "best" focal length of a zoom lens. But when the zoom lens starts moving various elements around those issues can be magnified and become more noticeable. For the vast majority of zoom lenses, the longest extreme of the focal length is also where the optical performance is poorest.
Roger Cicala has written a few blog entries that discuss these issues, which include the following:
Painting Zoom Lenses with a Broad Brush – Roger’s Law of Wide Zoom Relativity
Things You Didn’t Want to Know About Zoom Lenses
There is No Perfect Lens
While there are probably "better" copies of the Sony SEL18200LE out there, they're probably not that much better, and there are plenty that are worse than yours.
Do these photos indicate a lens problem, or am I expecting too much from my gear, or could there be another problem?
You are expecting a lot from a zoom lens with a greater than 10X focal length range that sells for about $750. If you want pixel peeping sharpness, go to higher end zooms with narrower zoom ranges or, even better, use very well corrected prime lenses, such as this $4,600, 2.5 pound, Zeiss Otus 85mm f/1.4 or a Zeiss Otus 55mm f/1.4 Distagon T*.