Visible crew/equipment: When the Batmobile is driving itself to Batman and Vicky Vale, you can clearly see a hand turning the steering wheel. (01:12:00)

Batman (1989)
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Directed by: Tim Burton
Starring: Michael Keaton, Jack Nicholson, Kim Basinger, Jack Palance, Michael Gough, Billy Dee Williams, Robert Wuhl
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Trivia: Sean Young was originally cast as Vicki Vale but broke her collarbone while filming a horse-riding scene with Michael Keaton. The scene was subsequently written out of the script when Kim Basinger took over the role.
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Answer: He could have looked up her address in the phone book. Just before Bruce arrives at Vikki's apartment, Joker asks Bob the Goon for - a phone book. Also he could have been tailing Bruce and found her apartment that way, after all he does show up not long after Bruce does.
Alan Keddie