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)
Visible crew/equipment: When Batman comes through the skylights in the museum just after Vicki throws water on Joker's face, you can see the stunt cable that lowers Batman down. Batman does use a system of cables and grappling hooks because he has no superpowers, but the cable lowering him down disappears as soon as he hits the ground. It was used to lower the actor down safely, not the character.
Visible crew/equipment: In the museum rescue scene, as Batman lifts Vicki up to ride the Gauntlet/zipline to safety, an extra supporting hand can be seen around her waist as they cruise out of the frame.
Visible crew/equipment: When Joker is being lifted by the helicopter at the end the lines from the safety harnesses that attach him to the ladder are briefly visible. (01:57:25)
Visible crew/equipment: Set lights are reflected in a building's second story window just before the Joker and his goons start tossing handfuls of cash to the crowd. (01:36:30)
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