Other mistake: When Cole is looking at the LAPD records, Billy Phelps has a birth-date of 9/16/63 and is listed as 28 years old, meaning the current date is at least 9/16/91. However, the first record, Rick Sabman, has a birth-date of 9/1/60 and is only listed as 30 years old, when he should be 31.
Other mistake: In the scene where 'Sergeant' Jack Travis is asking to see billy Phelps, he is addressed as a Sergeant, later when Lorna is showing the CCTV footage from the interrogation room, she calls him Lieutenant Jack Travis. Is he a sergeant or a lieutenant? Furthermore, given he is a former police officer, he wouldn't be allowed near the station, let alone be allowed to interrogate a suspect in police custody.
Other mistake: Murtaugh is in the bathtub in the end and his kids rush in to celebrate his retirement. He's supposedly naked. Later, he pulls his wife in with him and you can tell he is wearing black underwear.
Other mistake: After the shootout, where Rog kills his son's friend, Rog turns the kid's body over. He pulls his sunglasses off. The kid, who is supposedly dead, moves his eyes.
Other mistake: At the construction site, when the car rolls in empty. Not only is the windshield suddenly tinted, the car is also riddled with about 100 bullet-holes when only 1 or 2 guys fired a few bursts.
Other mistake: The end credits mis-spell St. Petersburg as "St. Petersberg".
Answer: She didn't want him to see that she was a fan of those comical idiots. She was supposed to be a tough nonsense internal affairs officer. She was in fact his soulmate, exactly like him, wild and crazy.