How do I start a new SMS conversation? All the messages I ever exchange with one number are listed as one conversation. How do I start a new conversation with someone on the same number? 

If this is an organisational thing, then I'd like to be able to use it as one and genuinely treat new subjects as new conversations. Or not to be told that every message I ever send someone is part of one long conversation when it isn't.
I don't particularly want to have to delete my entire message conversation with that person just to get rid of an error message; if anyone knows another way to get rid of the 'failed' I'd appreciate that too.


You don't, you just have to delete the message that is failing. Long press it, choose "Delete".


  How do I start a new conversation with someone on the same number?


How do you expect your phone to understand what messages belong in which category? The only way I see this working is if there's a function to put "all messages from now on" in a separate conversation, but that's not a feature that exists in the standard SMS application, and not in any app that I know of.

Dividing your past messages with a contact in two parts makes no sense, it would be even harder to find a message then if you can't remember what "conversation" you've put it in. Not only would you have to scroll back to see it, you would also have to pick the right category. Surely it's easier to sort the messages on a by-contact basis and just scroll.