Continuity mistake: Shaft gets approached during the credits by some bootlegger trying to sell him a watch. He flashes him a badge, which is held differently in closeup (finger up) compared to the full shot (just cupped in his palm). (00:02:30)
Revealing mistake: During the credit sequence with the iconic Isaac Hayes theme, occasionally passersby look into the camera, but given the camera placement and the amount of people involved it's hard to label that as mistake. At one point tho, around the 2:50 mark, some tall dude walks into frame and waves a "black power fist" for the camera - he couldn't be greeting Shaft with the gesture because he does it when Richard Roundtree has already walked well past him. (00:02:50)
Continuity mistake: A fight happens inside Shaft's office: a shattered glass noise can be heard, but the door is intact. That is, until the fight is over and the plaid coat man flies off the window. At that point the front door glass is shattered as well. Moreso, a shattered glass noise is heard when someone ends up against the wall, but the frames don't appear broken at any point. (00:10:35 - 00:11:10)
Continuity mistake: During the brawl in his office, Shaft sends the plaid coated man flying all over the table to the left of the window, right where there's a white paper bag. A moment later in the fight, that flimsy paper bag is still where it was, totally uncrushed by his butt. (00:10:40)
Continuity mistake: When the gangster with the plaid coat is strangling Shaft, the supposedly first-person shot shows him with his thumbs all the way up as if he were crushing his temples in a head vice - he is instead choking him, thumbs under the chin. (00:11:00)
Continuity mistake: During Bumpy's visit to Shaft's office, the crime boss is sometimes wearing his hat with the buckle on the left, other times with the buckle on the opposite side. (00:19:20 - 00:26:30)
Visible crew/equipment: When Bumpy hires Shaft to find his daughter, Bumpy gives Shaft an envelope with money, and when Shaft stands up you can see the bulge of the hidden microphone and wire at the front of Shaft's turtleneck sweater. When Bumpy leaves the office Shaft turns around and there's a bulge at the back of his waist, which is presumably the mic transmitter. (00:26:10)
Continuity mistake: When Shaft accepts Bumpy's case, Bumpy tosses the envelope on the desk and it lands on top of Shaft's playing cards. When Bumpy gets up, the envelope suddenly changes position. (00:26:15)
Continuity mistake: Shaft gets tipped by an informant about his case. He says "Stay loose, baby!" and gives him a raised fist salute walking away. But in the next shot he's still awkwardly giving him another raised fist, which then turns into a high-five. (00:30:45)
Continuity mistake: At the very beginning of the scene when Shaft is visiting Bumpy with Ben, Willy is playing solitaire. The very first transition between shots happens when Willy flips a card and lays it on the table, but the position of all the cards on said table have changed. (00:49:00)
Revealing mistake: When Shaft and his buds are sneaking into a building to save Bumpy's daughter, a pedestrian momentarily comes into the shot and then quickly steps out when he sees the camera crew. (01:18:45)
Suggested correction: I believe the entry refers to the initial rescue attempt, at 1:18:45. I am not entirely convinced that this is a legitimate goof though: the man sees 3 guys peeking into an alley, and he seems to rather stop and backtrack to check out whatever they are looking up, the exact opposite of 'stepping out'. It's still a rather amusing detail, though.
Continuity mistake: At the beginning, Shaft is crossing the street and a taxi jumps around between cuts. In the overhead shot, he passes the taxi and walks in front of a taxi, but in the level shot, he is in front of a brown car and giving it the finger.
Factual error: The calendar in the police office indicates Tuesday January 27th and Thursday January 29th. That was in 1970, but this story takes place in 1971.