The responsibility depends on the sale here folks. My company ships things to our customers FOB only. Freight on board means that once its left our shipping bay, it is theirs, and we are no longer responsible for it. IT depends on what the agreement was. A smart seller will put "Not responsible for damage durring shipping or lost/stolen packages." . I see it all the time on ebay. A smart buyer will pay the extra $$ for insurance.
Now in a dispute the burden of proof is up to each party. The seller must be able to prove he/she shipped it correctly, and the buyer must be able to prove otherwise.
If the seller did everything as he was supposed to and did insure things correctly then you are in fact SOL. I'm sorry but it UPS ****** this one up, its not his falt.
However if he is the one who made the **** up, then it is indeed his responsibility and he should take ownership for it. It sounds like in this situation it was.
As for the TPMS sensor and tread issue, that is his falt. A used set of TMPS sensors is about $100-$120, new they run over $200. You should save a copy of his add, all emails between you and him, and take photos of the crappy tires and missing tpms sensors so you can prove you didnt get what you paid for. Then do like someone else already said and send them back, insured with signature verification. Call ur CC company and do a charge back. Watch out for paypal. If they are connected to your account they might try and take the money out of ur checking account to recoup their loss. If you can prove what happened you will be fine.