I fail to see how BA are in any way to blame for this and I sincerely hope this man loses this case. BA have no obligation at all to get him back to LHR or to Granada at thier expense, no matter how much he insists. He paid to fly to Grenada and they got him there.
He booked, paid for and flew to Grenada. He may have wanted to go to Granada, but then he should have booked, paid for and indeed flown to Granada. The fact that these two destinations have similar names is irrelevant, passengers are responsible for making their bookings, or trusting a travel agent to do it for them. The airline will fly you to wherever you have a ticket for!
I refuse to believe that a travel agent booking wouldn't have shown a flight duration, I have never seen such a thing personally and I used to work on an airline ticket desk and saw all kinds of travel agent confirmations from the World Over. Every single one mentioned a flight duration, or at the very least a departure and arrival time, from that it's not hard to work out the flight duration.
This whole thing stinks of someone wanting to be rewarded for their own sheer stupidity. If I wanted a flight to BHX then I would make damn sure I didn't buy a ticket to BHM.