There is a lot of red tape involved in exhuming a body, Home Office permission is needed, so too the family. They would have known about it long before it happened. And for all involved to be there at the graveside was just farcical.
When Hardy gets a phone call during his interview, the other characters hear the phone ring and vibrate. When the phone is shown, it says "ringer off".
Alec was waiting outside Ellie's place to ask for help as she is walking to her car. Ellie throws her things on the passenger side seat while she is talking to Alec. As Ellie walks around the car to get in the driver's side she tells Alec to get in. Alec gets in the passenger side and just sits down. He didn't move Ellie's stuff off the passenger seat.
Ellie Miller is shown working as a traffic cop in the Valley of the Rocks, near Lynton. However, she later mentions that she lives in Exeter and is based at the police station there. Lynton is more than 60 miles from Exeter and is well out of the beat range of an Exeter-based traffic officer.