The main problem in accepting the paper's findings is that the effects seem to be too big and too fast. But this does not mean they are wrong. The general story they tell, which is consistent with lots of recent empirical papers about the incidence of the corporate tax, makes sense theoretically, as it posits that tax incidence gets shifted from mobile factors (capital) to relatively immobile factors (labor). This is essentially Tax Incidence 101.
I noted that the famous Harberger (1962) analysis of the corporate tax shows that, depending on the dynamics of the corporate versus non-corporate sectors (in particular, how they compare in substituting between labor and capital as productive inputs), it is actually theoretically possible for the obvious, Tax Incidence 101 outcome NOT to hold. E.g., in Harberger 1962, capital wouldn't have borne the burden of the corporate tax, even though he assumed the capital supply to be fixed, had the attributes of the corporate and non-corporate sectors been reversed. In the present international setting with worldwide capital mobility, this implies that the opposite result - capital bearing the tax despite its greater supply elasticity - could happen. But to get this result would in effect be like drawing an inside straight in poker - everything would have to work out just so, as seems unlikely in the abstract, especially if the line between the sectors is not sharply etched after all.
What to do with the corporate tax if labor bears it is less clear. One can't just repeal it, as in the context of an income tax it is a vital back-up to imposing the tax on individuals. Repeal the corporate tax while still taxing individuals on their income, and people will do tax planning games so their earnings disappear and pop up again, tax-free in the putatively corporate sector. Switching to consumption taxation might eliminate this problem and even permit continued progressivity (so long as individuals remain relatively immobile) but that doesn't seem likely to happen.