What are the best ways to find errors in a sequence of messages (strings)?
Not sure if I get your question right, as you didn't specify whether this is a theoretical problem or a practical.

Assuming it is practical problem, there are quite some algorithms (e.g. TCP) depending on which layer your messages are being send (if they are being send at all). 

Assuming it is more of a theorectial problem you can use stuff like the Hamming distance. 

Maybe check: Computer Networks by Andrew S. Tanenbaum