Character mistake: In the scene where the gun dealer is showing handguns to Travis, the dealer shows off a gun he says is a Walther PPK, but in fact is a Bersa Thunder, which has a differently shaped trigger-guard.
Other mistake: Travis built a special arm holster for a gun that allows him to pull a gun easily, popping it in hand while his arm is already outstretched. It's the weapon he prepared for in the iconic "You talkin' to me?" scene, and practices handshaking with it. We see a scene when he prepares to go kill the Senator cutting the sleeve of the shirt off. And yet, when the actual attempted hit is shown, Travis has his hand (the gun hand) inside his jacket, alerting security. (01:36:30)Sammo