In the "flashback" of the murder and in niece Elize's drawing, Daisy is being stabbed in a downward manner from above, but when she is found the first time, she has been stabbed in her rib cage, in an upward stroke. The police should have noticed this fact right away.
When the Commissioner takes off his jacket to assist in the search, his tie is long enough to reach to the waist of his trousers. When he discovers the body, his tie is now noticeably shorter.
When the police go to check Daisy's car, DI Mooney says that it's locked and so they can't get inside, but when they look in the car, the lock button is up on the passenger side, which means it's unlocked.
After discovering the body, the Commissioner and the Inspector move it about and search for clues. They should not be touching the body or even near it until the forensics personnel have completed their work.
Daisy's Mustang has Hawaii plates, though the island is St. Marie, and IRL the French island of Guadalupe.