The mistake was a relatively minor one, albeit one that had an impact on the OP's enjoyment of the flight. At the point the mistake is discovered it seems to me that the situation should be relatively easy to salvage, but it does not sound to me as though the crew handled the next bit very well. It's not clear what alternatives were offered, although clearly they did make some effort to accommodate the OP, but due to allergy the alternative was not feasible. The OP might need to expand on that in more detail. I would have have expected them to make every effort to cobble together something, including looking at CW meals etc., offering dessert, cheese etc. To be fair, most BA crews I've come across seem pretty good at such improvisation.
What's definitely not good is telling the other passenger. Very poor and unprofessional.
And of course the state of the cabin adds to the poor impression.
It just seems to me that this could have been de-escalated to the point of very much being a non-story, but instead the OP is left feeling very disappointed, which is a shame. Complaints about BA F are quite frequent. I think the main problem is not that is is a terrible product, but simply that too often the expectations are greater than what BA seemingly is able to or willing to deliver.