So I recently mistyped an ether payment address 0x6bEE6FCB3213146Aa38928B91eebEC6527B716E2 as 0x6cEE6FCB3213146Aa38928B91eebEC6527B716E2 so I by mistake typed c instead of b. My eyesight is bad and I struggle with this more and more recently. The transaction seems to have gone through (several confirmations) . I am guessing I have lost my money? I thought there was a checksum for detecting simple typos in the quoted addresses? Given that I can get the private key for the right address, would this allow me to more easily crack the private key for the wrong address that probably nobody has the private key for in any case?
I am guessing I have lost my money?
Yes, I'm afraid so.
I thought there was a checksum for detecting simple typos in the quoted addresses?
Originally Ethereum addresses had no inherent checksum. (See Why don't Ethereum addresses have checksums?.) An optional checksum implementation was later added under EIP-55, but not all exchanges and wallets implement this, so it's possible you've been unlucky and the sending wallet is lacking the implementation. (Thanks @WBT for pointing this out.)
Given that I can get the private key for the right address, would this allow me to more easily crack the private key for the wrong address...
No - the probability of finding any address is the same, regardless of how "close" it appears to yours.
For future reference, to prevent this happening again: Ethereum addresses weren't designed for human consumption (hence the lack of checksum). Humans aren't good with raw hexidecimal strings - there's far too much chance of making a transcription/transposition error. Never, ever type them by hand. Copy+paste is a better option. (Yes, you have to be able to trust your machine/clipboard.) Also have a look at BIP-39 mnemonics and QR codes.
You'll also notice on Etherscan that there's an icon next to the address. (I think some people called them Identicons. See Address unique icon.) If the wallet you sent from supports these icons, then it's a quick way to check the receiving address is correct. (i.e. Does it look like you expect it to look?)