A random person would never send you coins by mistake, it can only happen if they for some reason take your address from a block explorer, but the chance of it happening is extremely low. It's impossible to mistype an address, because it would invalidate the checksum and a transaction will fail.
Sending coins back is a bad idea, because the address might belong to a custodian, and if this custodian will be uncooperative, the coins will be lost. I'd rather wait and see if someone approaches me. I'd also post that I received coins by mistake on this forum and reddit to see if anyone would come to claim, but I won't specify the date, amount and addresses of the transaction.
Rather than mistyping the address, the person could simply send coins to another address on the Blockchain. This issue usually applies to ETC as I've seen some cases where people send ETH to ETC addresses. I think that this is due to lack of education, not knowing to separate a forked project from the original one. With QR codes and NFC tags available today, sending coins by mistake will no longer be an issue. I doubt anyone would want to type a whole ETH address manually, unless a computer without a webcam is being used (for scanning QR codes).
Nonetheless, the chances of someone sending you ETH by mistake are very little. I hope that as developers improve user experience on ETH wallets, people will be able to make better use of it. The combination of checksums, QR codes, and NFC tags could make the process of sending ETH easier. In case someone sends you 1 ETH by mistake, you can either hold onto it (as the crypto space is still widely unregulated) or simply send it back to its original owner. But I'm sure most people will choose the first option since they have no obligation of returning the coins due to the fact that the Blockchain is decentralized. As long as you put the "free coins" you've received to good use, there should be nothing to worry about. Just my thoughts