Deliberate mistake: While most of the German spoken in the movie is correct (even if with bad accent) there is a translation error in the scene at Yankee Stadium. The accent suggests that these bad guys were raised in the communist eastern Germany and previously served in the secret service "stasi." When the guy with the sniper rifle gets nervous and asks if he should shoot or not, the other one says,"Nein, wir brauchen den anderen", which would translate, "No, we need the other one", but the subtitles say, "We'll follow him", which they do.
Deliberate mistake: When McLane pulls out the phone he shot up after he and Zeus get into the Yugo there are a lot of coloured long curly cables hanging from the damaged phone. Mobile phones of this era would not have had any of these cables inside them, it is a deliberately made prop.
Chosen answer: He sees the reflection of his friend's badge number that he remembered from their conversation about the lottery earlier, so knows the badge was taken from his dead friend.
Captain Defenestrator