Something happened to the Falcon on his flight down to Mexico. He was never the same after he landed.
For the first 15 minutes or so of this movie -- set in a large U.S. city -- everything is terrific. The Falcon meets two beautiful women, commits two minor crimes, finds a corpse, gets wrongly accused of murder, escapes from custody and learns that something mysterious is going on south of the border. It doesn't all happen in exactly that order, but there's plenty of fast-paced fun.
But once the Falcon and one of the women fly to Mexico, the excitement levels off. The plot slows to a crawl. Events, including murders, seem almost random, and even the characters appear bored at time. At one point, the Falcon warns a Mexican gentleman that somebody may try to kill his daughter. The man shrugs off the tip and assures our hero that Mexico is a very safe place. He's not even curious about where the threat comes from!
The problem with the main part of this movie is that there's so much Mexico, there's no room left for mystery. There's travelogue-style footage of lakes and mountains, and some of it is very good. There are songs in Spanish, performances of masked Mexican dancers and shots of Mexican fishermen at work. There are even stereotypical "comic" Mexicans who talk like Speedy Gonzales. But there's no suspense, and the ending is very weak.
Considering when it was made, "The Falcon in Mexico" probably had a public relations component. During World War II, the U.S. government encouraged Hollywood to portray Latin America in a favorable light. But in a mystery movie, an exotic setting goes only so far. After a crackerjack start, this little whodunit is ultimately unsatisfying. It's at its weakest where it should have been strongest.