Mr Mac,
I'm a little confused as to where (and indeed when) you bought the gin? From your information I'm concluding that you bought it from the official airport Duty Free shop on the departures level and before the second security point at the boarding gate. This leaves me a little confused as they normally confiscate liquids from passengers at this checkpoint. Did they give you one of those security carrier bags at the duty free shop? If not I'm not sure how it got through the security point. If I remember correctly the staff at the security point are G4S and the gate staff are Swissport in Swissport uniforms. Having your gin confiscated at T5 is annoying, I recognise that, but to be honest I'm having a hard time pinning the blame on BA for that. I don't think it's a reasonable expectation for contract gate staff in Africa to police every passengers onward connections and confirm the suitability or otherwise of their DF purchases. It would be nice if they did, but this is Africa and I'm a realist.
You raise the issue of other carriers going the extra mile during the ash cloud, but you've kind of answered it yourself when you said "No ash cloud there". If Lufthansa have the flexibility to operate to China from Munich clear of an ash cloud shutdown then great. Unfortunately BA didn't, through no fault of BA, and if none of their aircraft can fly what do you expect them to do? There isn't capacity to book all of BA's passengers on other carriers, nor to set up much in the way of ad hoc flights should an window of opportunity arrive in the cloud. Nobody did more in the UK to pressure the CAA to lift the ash cloud restrictions, but you seem to be making a point that something that affects BA far more severely than LH was better handled than LH. I'm sure it was, just as BA handled flights to Germany a lot better than LH did when Lufty last went on strike.
I've read your post in detail and to be honest there are some things in there that are BAs fault, others that are not and are inherent to air travel, and some where the blame is unknown.
New York flight: Patchy food: definitely BA's fault. IFE broken: BA's fault but it happens on other carriers too, even Emirates. Bags misconnected: maybe BAs fault, hard to say*. Happens on other airlines too. Bags in JFK, you're in Chicago: Not BAs fault. The bags are sent to their destination airport then forward shipped from there. If you'd be staying some time in Chicago they'd have been sent there but it's hard to hit a moving target.
Nairobi: Alcoholic comment: BA/Contractors fault, not acceptable behaviour, nothing wrong with champagne at 10am in my book! IFE unavailable/poor food: see above. Cabin crew conversation to your liking: not BAs fault, and indeed try getting any form of conversation out of Singapore Girl. Duty Free confiscated: see above. Baggage misconnected: see above*
Boston: Bags delayed: BAs fault*. Downgraded: BAs fault but also happens on pretty much every single other airline in the world plus you'll have got your air miles back so effectively flew for free. No comment from Cabin Crew: not BAs fault. What would you actually expect them to do other than offer tea and sympathy?
*Mishandled bags. All airlines do it, every single one of them. And often you can actually get statistics as to how each airline performs. BA handles in excess of 99.5% of its bags at Heathrow correctly every day, with over 50% of passengers transferring. The vast majority of those 0.5% of mishandled bags are inbound to LHR on a non-BA flight and fail to meet BAs minimum connection time. The baggage system itself at T5 is operated by Heathrow, not BA. There have been two major failures of the system in the last month. The most recent was Heathrows fault. The earlier was due to a worldwide SITA fault which affected numerous airports worldwide. Each of those failures left BA with approximately 20,000 short-shipped bags. Imagine what a row of twenty suitcases looks like. Then times that by a thousand. Then think about how long it'll take to clear that backlog even if you threw all your spare resources at it.
You appear to have been exceptionally unlucky with your bags Mr Mac and I have every sympathy for you, but given that 99.5% of bags transit BAs Heathrow operation without delay each day then you really are a statistical outlier on the bad luck scale. Doesn't make it any better for you I know, but thats the maths of it. You may find a continental hub suits you better, especially if flying from the north, but Frankfurt has it's own problems and a friend who earned his AF/KLM Gold Card the hard way (in the cheap seats) will only travel with hand luggage these days.
In times of disruption I often hear praise for Emirates. I often wonder what people think would happen to their own businesses and livelihoods if a foreign owned competitor, backed by the state, with unlimited resources, low taxation and third world labour costs and social rights, was permitted to set itself up in their home market and flood it with a similar product. Perhaps I might ask them next time.