After you stop a recording take, each person in Uploads shows how much of their audio Magpie has received, such as 45:12 received. When an upload is incomplete, the message under the timer gives the same time, so you can see how much is still in that person's browser before you choose Use received audio. Two people with the same name can be told apart by their received time.
The review page also shows how much audio was received for each track.