When the guys visit Gramps he is seated in front of a game of checkers. When Starsky sits down in front of the old man the game pieces are now in different positions on the board.
About mid-way through, another taxi driver falls victim to the murderer and is killed whilst sitting in the drivers seat of his taxi. Yet when Starsky & Hutch arrive, the driver is sitting upright in the front passenger seat. The police would not re-position the body. The authorities then begin to transfer the deceased to a waiting hearse. It is only a fleeting glimpse, but at this point the actor playing him momentarily shifts his position as if to get out of the car.
Starsky is a cop undercover as a cab driver and on a sting. A passenger enters his cab and demands to be taken somewhere, but Starsky needs to stay put. Yet---after telling the passenger that he is waiting for someone---he lets himself be manipulated and bullied to drive him out of there. Highly implausible: 1) Again Starsky is a cop on a sting, not a cab driver. 2) He just told him he is waiting for someone: that means, to the passenger, that he is otherwise occupied by another paying passenger and not available to drive; he is on the meter already. Yet the man tells Starsky "I don't care, you're wasting your time." Who was wasting his time was him. Why Starsky didn't speak up and become assertive is one huge plot hole here. Not even a real cab driver would have driven the man, when waiting for another paying customer.
When Hutch releases the grandfather from the apartment bedroom, he mistakenly asks "Where's your son?" He then correctly asks, "Where's your grandson?"