The chunk which hits San Francisco was reported to be traveling at about 32,000 miles per hour. That's very credible for an orbital collision. However, the firey blob we see impact with the city was clearly traveling at about 500 miles per hour. Something traveling at 32,000 will not be seen before it hits. There certainly won't be any time for someone to hear a rumble (speed of sound is only about 700 miles per hour - anything faster than that you won't hear before it arrives).
At 00:52:11 in the movie, an operator in a military surveillance control room is reading aloud live coordinates of a fast-moving object on his radar screen. The content of the screen is shown full screen for 2 seconds. However what the "radar" screen displays is a plain DOS listing of root directory on his computer hard disk. As the operator supposedly gives additional information about speed and destination of the moving object, what we see is that he types "DIR /W" within an After Dark DOS Shell session and yet again the root directory is displayed. We can even see clearly that Win95 is installed on the computer.
The asteroid is destroyed by Dr. Corbett's anti-matter missile. Such a device would be a scientific impossibility to construct on Earth, since anti-matter would be mutually destroyed in a nuclear explosion with any matter it comes into contact with, and everything on Earth consists of ordinary matter.
When Reese and Tyrell go up to the trailer to talk to the woman linked to Payne, you can clearly see a face of a crew member reflected in the window closest to the door.
An asteroid the size of Kansas City is in close approach to Earth. It would have been detected by observatories all over the world, yet in the film the only people who seem to be aware of the imminent impact are some U.S. scientists and military personnel, even after chunks of the asteroid destroy a town in South America and the city of San Francisco.