Sid - I fear we may have been sidetracked a little here but I meant that your original 'The TFO has had a busy day today' is the preferred option to the equally correct 'The TFO's had a busy day today'.
I understand how to use an apostrophe and apologise for not including all possible uses of the apostrophe in a post on an internet forum.
Your plural is incorrect, it would be the TFOs' rubbish; your example is meaningless.
You see the pilots' mirror would mean the mirror belonging to two or more pilots; the pilot's mirror would mean the mirror belonging to just one pilot; and the pilot's able to pick an argument with a mirror would mean someone was talking about you.
You, of course, also forgot contraction as a place where an apostrophe may be used.
You may like to know that it is possession, not possesion; and it is omission, not ommission.