Assuming that the captain was part of the "operating crew" and not positioning, then yes he should by all means have put his tie on when he went down the back. I am an F/O for a major holiday charter airline and it is our company policy to always put our ties on whenever we go out the flight deck door. What we do on the flight deck is up to us - you can wear a baseball cap if you want - but on the other side of the door it is essential that you look professional. It is hard to keep the hair under control at times because of headsets but if you have a tie on it makes all the difference.
There is a huge number of captains I fly with who complain almost daily about the dress state and presentation of the passengers we carry (ie flip flops, tattoos from head to toe with a stud through the bridge of the nose to boot), and to not wear a tie when going down the back reduces us to that level. How can we possibly demand higher salaries in our pay deals when we present ourselves as if we are in the queue at the DHSS? This captain could be the greatest most talented and skilled pilot in the world which is great but if the passengers see a dishevelled mess than they will think the opposite and there are a great many people who are very nervous when flying and may decide to fly with another airline next time. Remember who pays the bills.
As far as the argument over whether or not he should be in the flight deck in the descent through the London TMA I would like to comment as well. It is of course possible that there was in fact no descent and "Zones" was mistaken, but assuming for a second that they were in the descent, yes the captain should be present during the descent. It is our company policy that as soon as the aircraft enters the descent (regardless of where in the world it is) both pilots must try to stay on the radio at all times (ie avoid calling handling agents etc) - sometimes it is not possible but we try - for the following very important reason: If only one pilot is maintaining a listening watch on frequency it is twice as likely that he/she will misunderstand a clearance to a flight level (ie will hear "descend FL160" when the actual instruction is "descend FL 170" ). In the London TMA it is one of the busiest terminal areas in the world and the controllers are working so hard that it is entirely possible that they may misunderstand the incorrect readback as well. Having two pilots "listening out" reduces this possibility drastically, and these mistakes do happen from time to time but are picked up by the other pilot. I don't care what anyone says - yes each pilot can fly the aircraft single handedly - but you must have two pilots listening out to ensure maximum safety and anything less is foolish and increases risk. Having one pilot not even in the flight deck during this critical phase of flight is obviously not conducive to safety. Coming out of the flight deck for a chat or a pee in the cruise is a different matter though - very low workload.
So, "Zones" you are not being harsh. If everything you suspect was actually true than you have every right to be upset. You, as a paying passenger, have the right to expect nothing but the best in terms of safety and I am afraid that this captain has let you down badly. Any so called "pilot" who thinks that it is OK for safety to be compromised in this manner is a safety hazard as well.
Lazlo