Argumentum ad logicam basically says that, even though an arguer used a false or faulty argument to try to prove a premise, it does not necessarily mean that the premise is wrong. The Fallacy Fallacy uses the following form: Argument A for the Conclusion C is fallacious; therefore, Conclusion C is false.
Example: If Galileo had argued that the Earth revolved around the Sun and that it did so because the Earth was trying to hide from the Moon, he would've been correct that the Earth revolved around the Sun but incorrect in his reasoning. Regardless of how disastrous his logic was, it can't override the facts. It would be fallacious of anyone to argue that the Earth doesn't revolve around the Sun because Galileo used faulty logic to determine that it does so.
To be fair, Galileo did not make that faulty explanation. I made that up for effect. :)
Example: For centuries, it was believed by mathematicians that the proposition known as 'Fermat's last theorem' was true, yet it took over 300 years for anyone to actually prove it. In the meantime, many invalid arguments were presented for it.
They were right, they just struggled to logically explain why. Their struggles still didn't make them wrong.
(Adapted from: http://www.fallacyfiles.org/fallfall.html)