If I mis-typed or left out some characters, what is the threshold where the address won't be valid? I know Bitcoin and some other addresses have some type of error correction built into the address. What is Monero's?
The odds of getting a 4-byte cryptographic checksum to match is roughly 1 in 4 billion, 2^32 = (2^8)^4. A Monero address provides a 4 byte cryptograph checksum for detecting errors (parity). No Hamming error correction services are provided. Monero addresses without payment addresses and multisig abilities are always 95 characters in length.
The last 5-bytes of the hex encoded representation of a Monero address are base58-encoded. The lower 4-bytes of hex characters represent the checksum while the last byte of public view key bleeds into the top portion of the ninth base58-encoded segment that contains the checksum.
For details on how a Monero address is constructed see the working example at the bottom of Constructing a Stealth Monero Address?. For this working example, the 9th base58-encoding of ffADD56816 (hex) is Vr5GCd (base58). The ff comes from the lower portion of the public view key 3c450f27cd6849d9130addb2c566d910c5ef9bf4cecaed547004496fda52a4ff, and the ADD56816 comes from top four bytes of a Keccak-256 bit hash the Monero Cryptonote prefix in hex (12) + public spend key in hex + public view key in hex.
A Monero wallet address is base58 encoded, and prior to encoding contains a four byte checksum.
This means that if you enter one or more characters incorrectly, there is only a one in 4.3 billion chance that the checksum will still validate.
The base58 encoded string will always be 95 characters long, so it cannot validate if you accidentally add or leave out any characters.
Note that the first character will communicate the address prefix, for which there are only 3 valid options for the live Monero network (regular, integrated and subaddress). Therefore you are even more restricted if attempting to change the first character of the address.