When Nick and George are driving in the Porsche, their seat belts are on/off between shots.
Errors in geography
In the end, Nick's plane lands in Frankfurt, Germany. However, the police cars have license plates from Munich ("F" vs. "M").
On the trading-floor, the hand-signals bear no relation to the ones used by real traders, and caused much amusement in stock-exchanges around the world.
When Nick faxes the forged documents to the auditor, the header on the fax is dated February 5, 1995. A few days later, a devastating earthquake rocks Kobe, Japan. The Kobe earthquake actually happened a few weeks earlier, on 17 January 1995.
Towards the end of the movie, in a scene where various newspapers were shown documenting the search for Leeson, a Chinese newspaper's caption for Leeson's picture actually reads "(Chinese Premier) Zhu Rongji Happily Meets (UK Prime Minister) Tony Blair".
In one of the club/bar scenes, Blur's "Song 2" is heard playing in the background. The events took place in 1995. "Song 2" was released in 1997.
When Nick is printing a letter for the auditor, the date says December 1994. He prints this on a Canon BJC-4550 printer, which had his first sale in 1996.
When they are driving the Porsche at speed there are a couple of shots which show the famous Irish Pub, Molly Malone's. The scene was set in 1994, and whilst Molly Malone's is the oldest Irish Pub in Singapore it was only established in 1995.