Just before Doc Martin lifts his son from his highchair he undoes his bib, which he repeats in the next shot.
Doc Martin checks the curate's neck for a pulse using his thumb. As the thumb has it's own pulse. A doctor would check for a pulse with the index finger and middle finger.
The pain of passing a kidney stone takes a long time before it passes through the bladder. First the stone "passes" from the kidney down towards the bladder, which is where the extreme pain comes from. Once it is inside the bladder, the pain is much less then the initial "drop" that makes people have to go to the ER. When a person is prescribed pain pills it's after the initial drop when the stone is in the bladder, and even then it's a matter of time (it could take weeks) before it passes from the bladder.