mosh sometimes fails to connect on ssh connections with mismatched ssh keys, ssh prompts are missing

@boulet- reported an issue (via IRC) where he had trouble connecting with mosh:

2016-05-15 15:53:58 Boulet Hi, I got some troubles with mosh : mosh user@ip -- tmux works fine but I can't do mosh user@ip -- tmux attach -> [mosh is exiting.] ..
2016-05-15 15:54:06 Boulet How to run a mosh client in debug ?
2016-05-15 15:54:49 achin i wonder if there is an error message from tmux, but mosh is eating it
2016-05-15 15:55:29 Boulet achin: if i run a classic mosh connection then tmux attach it works fine
2016-05-15 15:56:09 achin what if you do ssh -t user@ip -- tmux attach ?
2016-05-15 15:56:12 cgull It's a little awkward. Two things can help. 1: run mosh inside script, and look at the log after your session fails. 2: the --no-init flag will stop Mosh from clearing/switching screens on exit.
2016-05-15 15:56:46 cgull achin's suggestion is probably the first thing to try
2016-05-15 15:57:58 Boulet Go it, Warning: the RSA host key for '' differs from the key for the IP address '' ...
2016-05-15 15:58:01 Boulet thx achin !
2016-05-15 15:59:32 Boulet I didn't get why my mosh command without tmux attach works with the warning about host key ... strange thing
2016-05-15 16:00:01 achin i don't either
2016-05-15 16:02:18 cgull Is the message coming from the local ssh client, or from an ssh running in your remote tmux?
2016-05-15 16:04:02 Boulet cgull: from the local one
2016-05-15 18:08:35 cgull Boulet: I'm using another machine that has mismatched saved keys, and now I'm seeing a problem with mosh. But not always-- it seems to be intermittent. If I do "mosh remotehost" (no command) sometimes it works and sometimes I get no connection. Was it like this for you?
2016-05-15 18:09:26 cgull And do you have to type a password for this connection?
2016-05-15 18:12:07 cgull And what OS are you using on your client?
2016-05-15 18:14:26 Boulet cgull: i didn't get any trouble without command (I may retry testing), no password (publickey), client on OSX / server on archlinux
2016-05-15 18:15:17 Boulet Available for some tests but right now i'm going to sleep :)
2016-05-15 18:15:32 cgull It's kind of strange, especially since ssh shouldn't be working at all. That's OK, I'm just writing up a Github issue for now

I'm on an OS X client, FreeBSD server, and I'm running mosh remotehost; sometimes this works, sometimes it doesn't.

It'd also be good to better handle SSH's messages/prompts for security issues.

No files, tests, or entry points are named. Start by reproducing mosh remotehost on an OS X client with mismatched SSH keys, then trace the connection's SSH message and prompt handling; done means the connection behavior is reliable and relevant SSH warnings or prompts are visible.