Chet Walters mentions that he owns a "1975 Fairmont", however Ford did not introduce a vehicle by that name in the United States until 1978. (Ford did manufacture a Fairmont model in Australia in the mid-1970s, but that vehicle was never exported to the U.S.)
Near the end when Haru is apologizing to his partner as he is loaded onto the ambulance, the camera pans to a news reporter and you can clearly see a boom mic reflected in the vehicle's window behind her (though I guess they could chalk this one up to being the "news crews' equipment").
When Haru is disguised as a chef in the restaurant, he tosses a piece of shrimp up in the air and it lands on the inside of a woman's black shirt. When Haru retrieves the shrimp from her shirt with tongs it is hanging on the outside of her shirt.
When Gobei sits in the wheelchair with a broken arm, he manages use that arm for lifting it over his own head to take off his medal which he places around Haru's neck. He does this swiftly and without showing any pain, yet he complains about his broken arm sitting still when Haru hugs him.
After Haru shoots the spear, the platform he is standing on is pulled into the wall of the room with Alison and the bomb. The bomb falls to the floor, but is shown in the next shot to fall neatly onto the rolling platform. The platform is then shown to be pulled through a window, completely shattering the glass and leaving the surrounding wall intact. However, Haru is later shown to lean on and fall because of a piece of broken wall (which is exactly where the glass was shattered).
A grappling hook caught on the right wheel of Gobei's wheelchair causes him to be pulled by the bus. After the initial sequence (when the wheel is shown correctly to be stationary) the grappling hook is obviously pulling Gobei from elsewhere on the wheelchair as the wheel is now turning normally.
When Haru is demonstrating his sword technique for Joey in the hotel there is a vase of flowers on the table for the scene. After Haru is done with his sword demonstration the shot cuts back to Joey where there is now a large scattering of cut-up flowers on the floor despite Haru never touching the flowers while wielding the swords.
When Haru shoots the spear into the room where Alison/Sally is tied up, the spear passes in front of her from her left to her right. When Haru is pulled through the same room by the rope attached to the spear's platform he passes in front of her from her right to her left.
When Haru is looking in the phone book for "Tanley, Martin" you can tell that a small list of addresses was pasted over the real phone book page. The fake addresses are in a bolder font, they aren't alphabetical with the other addresses, the prefix is the fictional "555-", and the white bottom of the list slightly covers the next names listed.
As the truck explodes at the end of the bomb scene, you can see the strap that was attached to the front of the truck pull the truck for a small shock-like movement and release the truck as the explosion occurs.
When Haru is showing off his ninja skills to Sally Jones/Allison Page at the Tacha Guru Dojo and barely nicks the shelves holding the ancient warrior ashes, you can hear the sound of some sort of a spring that triggers the shelves to collapse and fall.
After Haru dries away from the Dojo after saying goodbye to his fellow ninjas at the end of the movie, Gobei's wheelchair is still attached to their vehicle. He hits an object and goes flying but he can clearly be seen being lifted up into the air. His hang time is unrealistically long as well.