This question was asked on Reddit a while ago:
When a node sends a transaction to the network and has the receiver as a contract, does every node execute the contract bytecode with the inputs to confirm the hash? Or does the first node receiving the transaction execute and create the transaction hash that's then distributed and is what's used for consensus. Basically, is the contract code executed once or many times for each transaction? I assume the it's the former if every node is running the EVM. — Reddit: Basic Questions About the Ethereum EVM and State Storage