Factual error: The professional hitmen murder their victim in the hospital with a silenced .38 revolver. You'd think the mob would know better. Silencers have absolutely no effect on revolvers. They only work on closed-chambered, automatic weapons.
Audio problem: During McGarrett's second visit to question the professor, in the midst of their conversation, something off-camera makes a very loud thump. Professionals that they are, Buddy Ebsen and Jack Lord carry on with their lines as though nothing has happened. But this looks just a bit odd, because you wonder why their characters aren't curious about the noise.