Unfortunately, I think it's pretty common. You just have to lift out the tray tables in First or Club and look in the slot - it will have the remnants of many meals inside. To be honest, I'm not sure what they can do about it with the seat designs. I can't see how it would be practical to remove all the tables and 'deep clean'. I've always turned a blind eye to that on the basis that if the seat itself is clean and the food served hygienically - c'est la vie...
It may be First but it's still public transport.