To answer your question we should consider few things…
1. Mechanical precision – if the adapter isn’t 100% accurate, user might experience several disorders – de-centering, focus shift, accidental light flare.
2. Material – Lens bodies are in general built from different materials with a mount being made from brass, steel, aluminum or even plastic. If the adapter is made from different material, in theory we can experience some deformations resulting from changes in temperature, or simply from mechanical intolerance. Cheap Chinese adapters, usually made from a thin metal, could be affected by large temperature oscillations.
3. Reflections – This is very often problem for any adapter, because in ideal case, inner surface of the tube part of the lens construction is part of the original lens design. It means that the level and character of the paint or special coating material inside the lens adapter, might not be best for all lenses that will be mounted on it. To reduce reflections to the minimum, one would need to know exact character of the light spread of the lens after the exit pupil (and distance to the film plane). In practice, cheap adapters have very basic matte paint inside and this can result in inner reflections, flaring and significant loss of contrast, especially toward the edges of the image.
In general, every extra piece of equipment, means more potential problems, including production tolerances, QC and above mentioned factual challenges. Each extra joint in the light path can cause lot of troubles…
On the other hand, we are far from being defect safe with a native mount lenses. Automation of the lens production, which is extremely demanding process in terms of accuracy and precision, doesn’t come for free. We can experience lot of “duds” on the shelves, even with the most expensive brands such as Zeiss or Leica.
My advise is thus – test your lens camera combination prior to the purchase whenever you can, don’t think too much about IQ perfection, because you’ll never reach 100% anyway and finally, don’t take all those lens tests, especially so called scientific (based on test charts and MTF calculation) too seriously. Roger Cicala from Lens Rentals is the guy who has lot of experience and I find his articles to be among best on the Internet (if not the best). You should however always read his article to the end. Here is what he has to say in a conclusion of his article about lens adapters intolerances and problems (tested mainly on optical bench, highly precise optical instrument with its own caveats):
“What Does It Mean in the Real World?
Like a lot of laboratory testing, probably not a lot. Adapters couldn’t all stink or people wouldn’t use them. Like a lot of tests, you can detect a very real difference in the lab that doesn’t make much difference at all in the real world.”
I have also many Leica R lenses and I am happily using them on my Sony E mount cameras.