There is a third unrelated problem. Probably more!
A replay attack? Problem with the block counter being updated? I give up. what is third thing? :D
Well, on closer inspection it seems like the MAC isn't actually an HMAC, but just SHA3. And since the padding isn't verified (because it can't be) that leaves it open to simple extension/truncation attacks (Crytopals challenges 29 and 30)?
Nope. It's safe to make a MAC out of a keyed SHA3 hash (one of the criteria for the SHA3 contest was that none of the hashes be vulnerable to length extension). Fun fact: that's also true of the "truncated" SHA2 variants (SHA2-384 and the like).
Huh, good to know. In that case I'm not sure. What is your last issue?