How many characters you need to mistype at minimum to get another valid address?
Check sum is a result of 2 hash-functions: SHA256 and RIPEMD160. The length of checksum is 4 bytes. Hash functions are indistinguishable from random oracle, so it is possible, if you make 1 mistake in non-checksum character, you get the same checksum. But probability of this is 1/2^32.

Added later: not exactly correct due to base58 encoding. Correction in the another answer.