In the beginning when Shaft is walking across a street, an overhead shot shows him walking past a taxi and nearly getting hit by a taxi. However, a street-level shot shows Shaft standing in front of and giving the finger to the brown car.
At the beginning of the movie, in Shaft's office, Shaft changes back and forth between a lighter brown coat and a dark coat. The difference can be seen by noticing the horizontal seam on the back of each coat, one is straight and the other is not.
When Shaft gets hit with the machine gun, one of the wounds is to his head - you can clearly see blood there. Yet after the doctor works on him and gets him patched up, all signs of the head wound have vanished - there's no scar or patch there.
The month calendar in Shaft's office is January 1971 (February 1971 is also posted on the wall in a "next month" style arrangement). But in Lt. Androzzi's office, the date calendar reads Tuesday January 27 and later Thursday January 29. 27 January 1971 was a Wednesday and 29 January 1971 was a Friday.
(27 and 29 January 1970 fell on a Tuesday and a Thursday).