The "old BA logo" is probably because a bag tag machine failed and was replaced with one from an old store cupboard somewhere. That sort of thing happens all the time - the only difference being that at Heathrow T5, all the printers were brand new when T5 opened. That, quite honestly, doesn't indicate any inferiority between Gatters, Heathrow Terminal 5 or Heathrow Terminal 3.
I am concerned, though, with the OP concerning the life-jacket and the reference later on to "passengers stealing them". As far as I was aware, the presence and serviceability oflifejackets and safety cards is checked by the cleaners as part of the "cabin dressing" before every flight. The cabin crew also check their presence, on a long haul flight, as part of the pre-boarding checks. On short-haul flights, a manadatory check of 5% of lifejacket stowages are checked prior to boarding.
In New Club World, I am told, the lifejacket should be stowed, in a pouch, in a drawer at your seat side.
Airlines all take the issue of stealing safety equipment very seriously. Anyone caught, red-handed, with a lifejacket or safety card in his possession by British Airways usually results in an immediate "ban from travel" - a huge problem if the traveller happens to be halfway through his itinerary!