In the beginning of the movie when Conklin races the other motorcycle, they shift to a higher gear about 15 times with a 5 gear bike. With that many gears on the back end, they would have been going about 300 MPH.
When Miku is visiting the bank to obtain the note plate, in every shot from her flat to the bank she is clearly wearing black hosiery. (Sometimes sheer, sometimes opaque.) As she strips to change, she is already wearing (under the teddy) nude/champagne coloured tights.
When Sato has Charlie cornered in the parking garage, and is about to behead him, he looks back at Conklin, and draws a weapon. That looks to be a Wakizashi (Japanese side-sword to accompany the Katana). As he rides off to behead Charlie, he is scraping along the ground a much larger sword (Katana).
When the Yakuza godfathers arrive for the climactic meeting at the vineyard, the sun is shining as they get out of their cars. In the reaction shot of Michael Douglas watching them, it is unmistakably raining.
In the nightclub scene when Masahiro walks over to Nick and Charlie's table, he is holding a cocktail with an umbrella in it. The cocktail umbrella keeps changing it's canopy shape, from convex to concave between shots.
Nick refers to Sato as "Say-toe" quite a few times, until someone corrects him, and after this he does say it right, but there is one instance before the correction where he does say "Sato", suggesting that this earlier scene may have possibly been filmed after.
Nick has more ice than scotch in his glass when he proposes a toast to "those gala crime fighters from internal affairs division." In the next shot when he takes a sip, however, there is more scotch than ice.
Towards the end of the film, in the section where Nick and Sato are fighting. Sato pushes Nick onto the bike wheel, and then they cut to Sato punching the ground. In the following shot you see Nick grimacing and in the background you see a blonde haired guy wearing a green tracksuit type top quickly duck behind a tree.
Nick vs. Sato mud fight at the end, Sato slams Nick, Sato throws a punch and misses then Nick gets up and behind him there is a brief appearance of someone moving aside by the tree, most likely a crew member of the movie.
At the start of the Nick versus Sato climatic fight scene, Nick fires his shotgun towards linens hanging on a line. The circular squib wiring is visible on the sheet right before the "bullet" tears a hole in it.
Right after the Stakeout scene, the woman is seen walking away. The scene the cuts from a fishing port in Osaka to what is suppose to be the Osaka City Center area. If you look closely at the signs in the city scene, You would be able to tell that the location was switched to Kobe.
Though the movie takes place in Osaka, Japan's second city, none of the Japanese characters speak in the Osaka dialect. Rather, they all speak the standardized dialect, which is based on the Tokyo accent. Persons from Osaka would normally speak standard Japanese to somebody from another region, but it would be almost unheard of, in particular in the underworld, amongst people from Osaka.
The paper signed on the airplane in Japanese is a real estate agreement. When they meet at the police station they are told they signed an insurance form. This however could be explained by the Japanese police captain's mixing up the English terms "real estate" and "insurance".
In several scenes, Japanese characters (and Nick) can be seen opening and shutting taxi doors. In fact, doors of Japanese taxis are always operated by the driver, through buttons near the driver's seat; so this would never happen. Nick, on the other hand, would not be expected to know this, since it is his first time in Japan.
In the movie, the detectives frequent a somewhat swanky looking night club. It is somewhat implausible that relatively low paid police officers would be able to afford a bar like that. In addition, the bar is owned by a known mobster (in fact the mobster even shows up). Japanese police officers would never openly go to a mob owned establishment (or one where mobsters hang out), as could result in a public relations scandal.
Masa comes to rescue Nick at the farmhouse, armed with a submachine gun. However, since Masa is suspended, there is no way he would be able to access, and take, a weapon, since officially issued guns are very strictly controlled within the Japanese police. In addition, Japanese police did not have submachine guns at the time of the movie.
When Sato was brought back from New York to Osaka by Nick and Charlie, the airplane seen in the scene was Northwest Airlines Boeing 747-200. However after they land when Nick try to catch Sato after being taken by fake cop, it is clearly seen that the aircraft registration was N159US. In reality N159US is a Northwest Airlines McDonnell Douglas DC-10-40 not a Boeing 747-200.
During the restaurant scene when Conklin is running out to chase the Yakuza, and fires on them with his weapon, he is using a snub-nose .357. If you watch later in the meatpacking district, when he is looking for Sato, he is only using a .38. He didn't have a second gun, they changed the weapon mid-scene.
The motorcycles are clearly small capacity (125, 250 or so) single cylinder trials bikes, probably two-strokes, but they produce the roar of a four-cylinder liter-size street racer. As part of the Yakuza initiation, new members will alter their bike to make as much noise as possible. They are then required to ride up and down a particular stretch of road revving their engine.
At the end where the plates of the $100 bill are shown under the shirt, it clearly shows the "1" of "100" next to the portrait of Franklin, but on the real $100 bill it's the last "0" of "100" next to Franklin.