"reverse mapping checking getaddrinfo for xxxxx failed" is a red herring; it just means that the forward and reverse DNS don't match which means the ISP sucks and nothing else.
You should fix /var/log/btmp, but that's also not important.
Now, the count of 23 SSH login attempts from one host is. Look around at topics here and Google on SSH security. Start by installing DenyHosts or Fail2Ban, to prevent people from getting more than (e.g.) 5 login attempts before being blocked.
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