There have been reports quoting the three teenagers saying the killer opened the driver side door and attempted to prop Paul Stine up behind the steering wheel before exiting the scene - but here we will be concentrating on the facts only contained within the police report.
There is a possibility that the Zodiac Killer wasn't wiping down either the front passenger door handle or the driver side door, as the front passenger door handle was not visible from the three teenagers position across the street, and the driver side door handle area may have been obscured by the Zodiac himself, with the three teenagers just having interpreted his actions based upon him holding what was considered to be a white rag or handkerchief. It could simply have been the Zodiac carrying the section of Paul Stine's shirt. After securing a piece of shirt and exiting the front passenger side door, the Zodiac Killer could have immediately left the crime scene up Cherry Street, but he didn't. The fact that he traveled around the taxicab to the driver side door, without opening it, does not leave many options as to why he performed this action, other than wiping away fingerprints - and suggests the interpretation of events by the three teenagers was in fact correct.
Fingerprints were in fact discovered on the rear doors and any attempt to wipe these either failed or were never performed. Would fingerprints on the rear passenger doors prove to be incriminating evidence? - after all it was a taxicab. However, fingerprints on the front doors, in view of a piece of the taxicab driver's shirt being torn off, may have been a little harder to explain.
There is a logical course of events that may explain a murder at Washington and Cherry Street, explain the blood pattern on Paul Stine's shirt and crucially the bloody fingerprints on the post to the rear of the driver side door. As Paul Stine parked up at the Washington and Cherry Street intersection, the Zodiac placed the gun close to Paul Stine's head and fired. Back spatter from the wound would have struck Zodiac's hand and gun, depositing blood onto both. At this point, he could have just left the scene - but his objective was to secure a trophy - so he now had to access the front of the taxicab. In view of the bloody prints on the left post of the taxicab, this may suggest his possible route.