The murder took place well into the evening when it was dark, this is known because Charlie's call with him breathing went through when Mary was outside when Crystal left. The traffic camera photo of Crystal near the beach house from around the time of the murder showed it was broad daylight.
The police say Charlie's texts were delayed due to no/low cell service, but when Mary calls his phone from the beach house immediately after the text it rings right away. If there was no/low service, she would have reached his voice mail.
Police had phone records from Charlie's phone and would have tracked Mary's phone as well. Her phone's location would have allowed them to exclude her as a suspect, yet she is questioned well beyond this point as if she were a suspect. This is a plot hole, as by the time DNA evidence had been analyzed they would have all of the phone records.
Crystal was with Mary at the time of the murder, so she could not have been photographed near the beach house around the same time.
A warrant is not required for a consensual interview in a police investigation. An attorney would know this, so Susan's question to the detective when he was interviewing Mary at her home was improper.