For Major Dabney, it was while he was on the set of the movie chronicling the story of the Scarlet Strangler from decades prior. As one of the experts hired for the production, financed by Bruce Wayne, Dabney was joined by script girl Margo Cantrell and demolitions expert Mick Murdock. The trio aided Batman of Earth-One in discovering who the Strangler really was who reappeared to prey upon London's women... turns out it was the father of the film's director and the son of the original Strangler. The team was labeled the Bat-Squad, ready to help the Dark Knight if ever a need presented itself once more. It never did.
For Inspector Erskine Hawkins, it was while he was attempting to solve one final mystery... who was Superman? When he was out witted by Earth-Two's Man of Steel, he moved on to a hundred year old mystery which led to the appearance of a modern day Guy Fawkes who was really a crook named Roddy Greene. Although Clark almost believed that Hawkins finally stumbled upon his secret identity, Kent was relieved to year that Erskine was fooled by an action that Superman had set in motion at the same time that his mild-mannered alter ego was present. Since he couldn't reconcile his prey being in two places at once, he shook if off as proof that he was wrong about Superman's secret identity.