The halting problem in Ethereum is "solved" (more like "dealth with") by a very simple technique: every EVM instruction has a cost and you have to provide "gas"

The halting problem in Ethereum is "solved" (more like "dealth with") by a very simple technique: every EVM instruction has a cost and you have to provide "gas" to run your smart contract. If you don't provide enough gas, your contract call has zero effect and all the gas you paid is lost. A contract call that would misbehave is guaranteed to halt: not by itself, but by the EVM, which, when the contract call eventually runs out of gas, shall take care of halting it. It's pretty nice I'd say.