the joiners arse is not covered he should use 18mm or plastic ply,he is responsable for the floor and not you,tiling is a finish,not a preporation,as long as you are happy there was no obvious bounce in the floor,your okay as for lack of adhesive in the corner of a tile,thats not an issue as long as you re-do it.legally he has to pay you,in the first instance he has to give you the oppertunity to put it right if he can prove your at fault,if he says he does not want you to put it right,then you both have to agree on someone indepedent to put it right at an agreed cost,then pay you the remainder of your invoice,if he does'nt he will automatically loose in a small claims court,any work to the floating floor is not your cost as this is considered as betterment,in the last 6 years i have taken 3 people to court and won on this basis,i have just issued a summons today against a greek restaraunt who bumped me for £1,905 of which £1,140 is materials,its always people in business that seem to do it,domestic always pay,stand your ground