Read the report and I cannot help but think it will be slightly more than just a smelly poo...the captain isn't going to go into great detail as to what the issue is, but I'd wager it was a blocked of overflowing toilet, which needs to be cleaned up as soon as possible otherwise it will potential do a massive amount of damage to the airframe and could result in it being out of services for much longer than a simple system repair, as cabin fittings would need to be removed to be deep cleaned to make sure there's no risk of corrosion etc...
As to connections, if any were missed the airline will have to make sure they get to destination, well assuming it's part of the same booking, if not they could be seriously out of pocket, I'm not sure if or what interline/codeshare agreements BA have with EK or any other carrier who could be offering connections at DXB, they likely still have agreements with QF but beyond that I'm not sure I'd wager on that flight the majority will just have tickets between LHR and DXB as frankly of your connecting via DXB you'd fly EK