As each occurrence happened when a member of staff was trying to restrain him or not bend to his will, I believe it was simply his not-so-subtle way of reminding them that he had the power to remove them from their jobs at his whim, should they question his actions again:
With the nurse:
Um, Mr Smith, I'm just wondering, maybe this isn't a suitable subject for the children.
Nurse Cornish, how long have you been with us now?
Seven years.
Seven years. OK.
And in the morgue:
Everyone out.
Mr Smith, we're actually in the middle of something.
Saheed, isn't it?
Saheed, yes.
How long have you been working here now?
Four years.
Four years. Well, that's a long time, isn't it? Four years!