[Cryptography] How does bitcoin find if a transaction output has already been used.

[Garlo Nicon]

"how does verification work?"

Each node collects transactions and decides on its own if it will be
included in the new block or not.

"what if the node that won the block mine Didn't do that work"

If the community accept incorrect transaction, it will be accepted. It
is just very simple computing-power-based voting and validating
everything, nothing else.

"we Wait until 'someone else' finds the mistake? then what?"

If some node finds the mistake, it rejects that block. If nodes
sharing more than half computing power reject it, all future blocks
from that point will be rejected. But if not, then fixing this mistake
will be harder and harder, because each new block adds one more
confirmation.

"who the heck checks if the verifiers checked?"
"where's the procedure to assure it's correct?"
"who verifies Contracts?"
"who verifies ACLs for blockchain DBs?"

Nobody checks it, there is no procedure. It is just like voting in
democracy. The community is voting and if they approve something, it
will be approved. If not, the chain can be hard-forked between two
groups of nodes: accepting something or rejecting it. The longest
chain always wins, but if another chain is still getting longer and
longer, it is sooner or later called altcoin.