In the scene at the fitness studio where Viktor 'Rosta' Rostavili's girlfriend works, people are exercising to music. The record they are dancing to is Ramos - Jackin' National Anthem. This is a very early House Music track. House music originated in Chicago where the film is set, but at that time would not have been well known outside of Chicago. Chicago spawned this music genre and this is the earliest use of House Music in mainstream movies. Around the time of the making of this film, Acid House was just starting. This music was also from Chicago but relatively unknown outside the city at the time was produced using a Japanese synthesizer called a Roland TB-303. 303 is also the hotel room number that Arnold Schwarzenegger stays in.
At the beginning of the movie, when Arnold jumps out of the sauna window with one of the Villains you can clearly see a stunt doubler instead of Arnold.
At the funeral of Danko's partner, the year of death on his tomb stone says 1988. Later on, when Danko checks in at a motel, the date he writes in the book is somewhere in 1987.
The police mentioned he would have a "nice" room in a upper class hotel. Ivan being a soviet would much rather live in a room similar to his home accommodations. It also helps to prevent being poisoned by western influences of capitalism.Notice how poorly he responds to the pay per view TV.There's more to it than that, however. Victor was arrested close to the hotel.Victor had been pulled over for running a red light, whereupon the arresting officers found out that he was driving without a license and illegally possessed a handgun.In addition to being arrested close to the hotel, Victor had also been lodging there before his arrest. Ivan checks into the same room that Victor was using, presumably to find any additional evidence and clues that could be used against his fugitive.