Stan's bank card at the crime scene

None, it was just to get the story going. Rosie had it I guess in her pocket and it fell out while she was running. It made it look like Stan was the killer at first glance

It gave them a name to start the investigation with. We were meant to believe Stan was the murderer or had been murdered along with whom ever the sweater belonged to.

I thought they were going to refer back to it when they found the footage of the casino ATM or the fact she had a lot of money saved (ie she stole it from Stan)