Obvious solution would be to put up a lot of surveillance cameras, as developed by Dr. Science in government employ, to catch the do-gooders in action. If someone breaks into the warehouse, and Captain Goodguy follows them, and later leaves them tied up outside it, the circumstantial evidence inside the warehouse would probably be enough to convict.
Also lend itself to 1984 style surveillance, which would certainly inspire some to stay vigilantes. Plus might lead to either discovering who Captain Goodguy is, or accusations of collusion with the good captain on part of the authorities.
Or -- hmmm -- Dr. Science could be a vigilante himself, providing them with cameras so they could leave behind records. Much to-do, perhaps, about whether they could be relied on, but if only the vigilantes could take down the supervillains, they wouldn't have much choice.