Of course there are some cons. If there weren't, everybody would do it all the time. :-)

For some obvious cons, consider that a medium format lens will almost always be:

• larger
• heavier
• more expensive, and
• lower resolution

...than a lens built specifically for 35mm.

As for the specific questions you asked:

• Can the greater field of view be a source of some internal reflections in the camera body?

At least in theory it undoubtedly can. I've never seen a substantial loss of contrast though. I don't remember with certainty, but I'd more or less expect an adapter to include some baffling to minimize the amount of light transmitted outside the film/sensor rectangle.

• How does the focus range change with such a mount (especially ability to focus at infinity)? Are the lens adapters designed in such a way that this focus range can remain unchanged?

At least in the cases I've seen, infinity focus wasn't a problem at all. Every medium format camera of which I'm aware has a considerably longer registration distance than an 35mm camera, so getting the lens close enough to the film plane is no problem at all.

• Does greater field imply that the 35mm image is less prone to lens aberrations?

In theory it might. In reality, I've seen little or no real difference.

I think I've already covered a number of the other obvious disadvantages above, so we probably don't need to repeat them specifically as answers to your last question.