An incomplete vaccine can apply evolutionary pressure on the virus. From my understanding that's probably not so likely if just a few scientists use their own vaccine (someone more knowledgeable please correct me if I'm wrong), but may be a valid concern regarding some countries rushing through vaccines that have had limited testing. (eg. the Russia example)

I'm just repeating what I've heard, as I don't have specialist knowledge of this area, but one logical problem that occurred to me about this was whether the breadth of coverage of a vaccine is even testable. I would love to know how that gets tested in trials, because what I've heard about how vaccines are assessed has sounded a lot more primitive than anything that would indicate breadth of immunity.