'Changing trains in New Haven'
At the end of the movie, when Henry finally calls Leona from a pay phone, he states--apparently truthfully--that he's in New Haven, where he claims to be changing trains in the course of his alleged trip from New York to Boston. That makes little sense: In the late forties, there was almost no reason that someone would have needed to change trains at New Haven while going from New York to Boston (not that there's much possible reason today either). And Leona would almost certainly have been aware of that, and therefore taken Henry's statement as an indication that even more strangeness was going on, since although she was originally from the Chicago area, she'd apparently gone to an Eastern college whose students routinely socialized with students from Yale (in New Haven) and Harvard (in the Boston area), so that she probably would at least have had some knowledge of the New York-to-Boston service of the New York, New Haven and Hartford Railroad (which was essentially the only New York-to-Boston rail service there was). The only reason I can imagine for Henry to have needed to change at New Haven for his alleged Boston trip would be that he'd started his journey not in midtown Manhattan, at Grand Central Terminal or Pennsylvania Station, but at some smaller station to the northeast, where the high-quality express train or sleeping-car-equipped overnight train to Boston he presumably wanted to take for the bulk of the journey didn't stop; so that he took some sort of local train from that smaller station to New Haven, and then changed to his high-quality express train or sleeping-car-equipped overnight train there. (The equivalent today would be to take a Metro-North commuter train or an Amtrak "Northeast Regional" train from a smaller station to New Haven, and then change to an Amtrak Acela train there--though such a change could also be made at the Stamford, Connecticut station.) But if Henry had mentioned such an explanation to Leona, she would have picked up on it as suspicious as well: What reason would he have had to board at some small station northeast of midtown Manhattan?
(Today, in 2014, an additional conceivable reason to start one's Boston trip on Metro-North and then change to Amtrak, at New Haven or elsewhere, would be if for some reason one definitely wanted to start out from Grand Central Terminal rather than Pennsylvania Station--since today Grand Central hosts Metro-North trains to New Haven, but doesn't host any Boston trains at all. Prior to early 1971, though, both Grand Central Terminal and Penn Station hosted trains to and from Boston. And just to clarify the situation for those who aren't familiar with the rail network of the greater New York City area, the rail lines of Grand Central Terminal and Pennsylvania Station aren't directly connected: rather, the two stations send out their northeast-bound trains--that is to say, trains going in the direction of New Haven--on separate rail lines, which don't come together until New Rochelle, New York.)
What would have made much more sense would have been if Henry had said that he was making his phone call while his train was changing engines. From 1914 until 2000, trains from New York to Boston had to change from electric engines to conventional locomotives (steam originally, later diesel-electric) at New Haven, since the electric wires that powered the electric engines ended there. The process required a stay of several minutes in the station, a stay that could end up being even longer if the train arrived in the station early.