Deliberate mistake: When the chase enters the tunnel blocked on the other end by the tanks, the Yakuza are firing machine guns at Daniel's taxi. The spent ammunition drops straight to the floor as if someone has thrown a handfull of shells. If they were fired from a fast moving car they would scatter all over the place.
Continuity mistake: When Daniel is being chased by the Yakuzi in their black Mitsubishi Lancer Evo 6s, one of their Lancers crashes into the tanks. The car used for that crash is however a Lancer Evo 4, which is older than the Evo 6, and has a different front bumper, bonnet and rear spoiler.
Continuity mistake: When Petra is fighting the three ninjas, her thong underwear is white at the beginning of the sequence, but changes to a flesh colour during the scene.
Continuity mistake: When Daniel arrives at Lilly's house (precisely when he takes the shirt out of the car) stock hubcaps are visible, whereas the car normally has alloy rims.
Revealing mistake: When Daniel is being chased along the rail tracks, both the Peugeot and the Mitsubishis' wheels change from road wheels to train wheels (with fake tyres on) and then back again when they move back onto the gravel. Clever cars...
Other mistake: When the airbags are deployed on the "indestructible" Peugeot they stay inflated, making it difficult to get the driver out of the car. Comedic effect aside, real airbags do not deploy when the vehicle is stationary or hit by a hand on the roof and also begin to deflate immediately after deployment due to the gasses cooling and leaking out of the vent(s) in the bag. A previous correction speculating about modified airbags cannot be proved and is irrelevant as they are a legal safety feature of the vehicle and cannot be modified.
Continuity mistake: When Daniel gives Lilly's dad a lift to the airport to meet the arriving guests, he transforms the taxi. We see all the transformation take place, but when he lowers the car down from the gas rams the front spoiler is not there.