Bitcoin has checksumming so it's difficult to mistype an address. Do z and t addresses have the same feature?
Yes, they both do. I don't think I've seen any base58 encoded strings that weren't checksummed - it's actually referred to as base58check encoding. There are only a few coins (like Ethereum) that get by with only raw data for key representation... https://github.com/zcash/zcash/wiki/specification