Goofs

Owen shows no sign of the bullet wound to his shoulder he received from Ianto in the previous episode, Captain Jack Harkness (2007).

In the previous episode, after Owen was shot, the blood on his face went from his mouth towards his ear, but an hour later in 'Dead Man Walking', the blood makes a line from his mouth to his chin.

When Martha starts the autopsy on Owen, the first thing she picks up is a bone saw. An autopsy would begin with opening the body up with a scalpel, usually a 'Y' incision from the shoulder to the groin.

Ianto announces that he's "getting no life signs" from Owen's body and the flat-line buzz is heard. When the camera flashes back to Owen', you see that he's not connected to any machines. Monitoring equipment needs to be connected to a body to show life signs. Torchwood has access to alien technology that may not need a physical connection to a body to work.

At 7:23, when Owen is still supposedly dead, his left shoulder/arm makes an obvious move.

The episode starts with Martha performing an autopsy on Owen. As Owen worked for Torchwood and his body would be put into cold storage and no formal record of his death made public, an autopsy would be pointless, especially as they know how he died - they saw him get shot in the chest.