Roger Penrose is not merely saying that quantum mechanics is wrong. Instead it would be more fair to say that he views quantum mechanics as an incomplete theory, and one that should be continually challenged.
It's like Newtonian mechanics. Newtonian mechanics is correct, within its domain (for velocities much less than the speed of light). No one argues with the predictions of Newtonian mechanics within their domain. Einstein's achievement with special relativity, then, wasn't showing that Newtonian mechanics was wrong; instead, he just showed the world the true extent of its domain, and developed a theory (special relativity) that generalized Newtonian mechanics to a larger domain (velocities less than the speed of light). It's terribly unfair to Newtonian mechanics to call it 'wrong' in the same way that the statement 2+2=5 is 'wrong'.
Similarly, the fantastic experimental success of quantum mechanics ensures that it would be unfair to call quantum mechanics 'wrong'. Incomplete? Certainly. Worthy of being challenged? Absolutely. Is it taken as gospel by too many physicists? Probably. But is quantum mechanics wrong? No, decades of successful experiments, and practically the entire modern electronics industry, would disagree with that sentiment. The problem is that we just don't know where the domain of quantum mechanics ends, nor the more general theory that will take its place.