Writing down your key is not a good idea as even one "typo" would cause your entire "key" (it wouldn't actually be a key anymore) worthless
Actually, a private key is just a big number (up to 2^256, or more correctly 0xFFFF FFFF FFFF FFFF FFFF FFFF FFFF FFFE BAAE DCE6 AF48 A03B BFD2 5E8C D036 4141).
So with a typo, you would get another valid key, which statistically speaking should be almost sure to be associated with an empty address.
depending on what "language" the key is written in it may not translate back over to HEX format within the possible ranges of private keys
Also as you said, the new private key would almost certainly be worthless as it would (almost) certainly be associated with an address with no (spent or unspent) inputs