I used to work for a Mazda dealer, and all the parts delivery from Mazda UK came by TNT. We always signed the slip 'unchecked' or 'advised 40 boxes, recieved 39' or 'one box broken open' ETC.
The del frequently ran to 30 or 40 seperate boxes, and maybe 200 different items. Needless to say the TNT driver did not want to wait for 2 hours while we checked off the del against the advice note.
Legally i dont know where you would stand, but i never had a problem for claiming for missing parts.
The asumption was that as the driver won't wait for you to check it, they have to take your word about missings bits.