Trivia: Michael Keaton had to wear a separate cowl with shorter ears for the scenes where he gets in and out of the Batmobile. The vehicle's sliding canopy feature had been designed based on his pre-costume measurements, and it was only once filming had started that the crew realised they hadn't thought to measure him again while in the batsuit, so they could account for how much extra height the ears added.
Trivia: The Batmobile went through the full process of being designed, drawn up, signed off on, and built at full scale, before someone thought to ask "Wait, where's the door?" Since the designs called for giant intake vents where the doors were supposed to be, nobody had thought about how Batman was supposed to get in and out of his vehicle. The team quickly came up with the alternate idea of having the Batmobile's canopy slide open like a jet fighter so he could climb in.
Answer: He was suspicious, but when she first entered the penthouse and Grissom said to leave their business meeting, he noticed the sexy facial exchange Alicia and Jack gave each other.