When Raymond calls Marion from the pay phone, he tells the operator to place a collect call. When Marion answers the phone she immediately starts talking to him. The operator never told her it was a collect call and asked if she would accept it before connecting them.
Mr. Brown arrives when the police are processing the crime scene and medical personnel are removing Mrs. Brown's body. When Mr. Brown goes for a drink, Lt. Storber informs him that she died from cyanide in the Scotch. Since they had apparently only just discovered the body, they wouldn't have had time to test the liquor for any poison, and the Scotch would have masked any odors.
Marion killed her victims by putting the poison into the bottle of booze. This should have struck the police as very odd, as there is no logical reason for someone to put the poison into the whole bottle. Someone committing suicide would normally only poison their drink and not the whole bottle.