Factual error: In a scene in a bar the music playing is Blur's Song 2, which wasn't released until 1998 and a Kula Shaker song which wasn't released until 1996, by which time Nick Leeson was firmly in prison.
Continuity mistake: Although the exterior shots were clearly filmed in the appropriate locations in Singapore (allowing for the fact that filming must have taken place early on Sunday mornings), interiors were shot largely in the UK. The error I noticed in particular arose in a sequence where McGregor, playing Leeson, is in Barings' office in Singapore and needs to go to the Mens' Room. However, the sign on the door is nothing like the standard Mens' toilet sign in Singapore (which is much more rounded and has the man's legs next to each other, while the sign shown has the man's legs apart). What's worse, in Singapore all the urinals in mens' toilets have a switch, button or electronic device to flush them after use (I believe that it's an offence to leave one unflushed after use). However, the urinals shown in the scene had the standard British cistern and no devices to flush them after use.
Factual error: Before his arrest, the police cars approaching Nick's plane in Frankfurt airport bear Munich (M) number plates instead of F for Frankfurt.