Where you on seperate tickets as that would explain why bmi could not check you through?
I used to travel on BD/SK tickets quite a lot. For some reason, only some of the time, I couldnt check in online for my bmi flights. No big deal - check in at the airport.
However, if you dare to try to check in on flysas.com, it always worked for their legs and you got the seat you wanted. However for some reason bmi, could no longer print a boarding pass for the sk leg. There was some weird stuff happening within the IT systems. However, back to the point, even with these difficulties, I never had to collect my bags when transitting in LHR - hence why I think you were maybe on seperate tickets?
I think you need to blame the dirty scrote who left the chewing gum there instead of bmi. What was wrong with using the sick bag or sticking it in with their rubbish?
Poor show on catering.. but whats new?
You would have had to go through security in T3 again anyway, even if connecting via FCC.