What disease is on this Walnut tree?

As you're not in the UK, I can only tell you what diseases walnut suffers from typically here. Check out Walnut blotch - this is a fungal infection, usually treated with a copper based insecticide (if they still allow that - Europe's banned loads of stuff, but you may be able to get it, if you decide that's the problem.) I think the RHS (Royal Horticultural Society) has a pests and diseases catalogue, but can't swear to it.
I have to say, though, that the evidence on display in the photo looks like some kind of boring insect, or a leaf miner of some kind. There is something called Walnut Blister Mite, but you usually get what look like "blistered" areas on the leaves with that.
There's another thing called Walnut Soft Shell - don't know if the nuts on your tree ever form hard shells? Or maybe they're not on the tree long enough to do it. Check it out online anyway

do all the nuts fall or only some? many fruit trees undergo 'june drop' and is due to there being too much fruit for the plant to cope with. the plant doesnt produce enough plant hormones so the smaller more immature fruit drop off.