You are painting a scenario that could theoretically become an issue if vaccination somehow got stuck at some point close to or far beyond the 50% mark for some reason. E.g. to deliberately exclude some part of the population, or in some "the vaccine is actually a carrier for something else" movie plot. But if the limits of vaccination are just the confines of ramp-up and particularly if priority is given to the elderly, it's just a phantom fear. Not allowed to go to work unless you are older than 75? Right...

At first glance forgery seems like a very real threat considering how hard it is to tell vaccine from sodium chloride (entire testing procedures are based on this), but the same difficulty is also working against a black market: why pay if the seller can't give event the slightest indication that it's not a fake and the fake has no intrinsic value at all? You'd have to fake the distribution structures and not the product and an elaborate fake structure isn't something that suddenly pops up from some dark market investment, it could only evolve from simpler black market schemes. But those won't happen, at least not in time (except maybe in places with a truly corrupt regular distribution system, where it would start with "redistributed" real vaccine and then slowly shift over to fakes)