The closeup of the keys when Ford Fairlane arrives at the club at the beginning shows a much newer style of Ford key that what was made for that car. In that shot, you can see the correct style on the opposite side of the key ring (farthest from the camera view).
At the beginning of the film, when Ford is telling the backstory of rock star Bobby Black when he dies on stage, the song Bobby sings includes the line "No she don't give a... No she don't give a SHIT!" Later, when Ford is watching MTV and sees Zuzu Petals in Bobby's music video, we hear the same lyric, including the word "SHIT". It is a violation of FCC rules to air an obscenity on a broadcast without censoring the word. MTV would be fined and/or reprimanded for airing an uncut version of the lyric. (Ironically, Andrew Dice Clay was banned from MTV for life after using obscene language on the MTV Music Video Awards, thus getting MTV in trouble with the FCC.)
Johnny tells Ford to meet him at the radio station at 6:00 p.m. When Ford parks outside the station, the sky is dark. As we learn later in the film, the story is taking place in late July. Sunset in Los Angeles in late July is about 8:00 p.m., so it shouldn't have been dark yet.