There's something bugging me in this episode - the speeding ticket. I'm assuming that The lawyers partner was wearing the mask. Why was she wearing the mask at the time of the murder to provide an alibi? She didn't even know the lawyer killed the girl til after the event. Am I missing something?

After the murder has happened she refers to the mask thing, says something like, "that's why you sent me on that strange errand." Viewer who had never seen the episode before would not realise.