Since lots of filenames have changed you should check that any manually installed versions prior to 1.13.0 are removed. Otherwise you will have startup problems.
The default output logger text has now colored output if the output terminal supports it.
The -F option no longer suppresses normal output. The old behaviour can be restored by giving the option -onone.
The --status option is now the default and has been deprecated. The old behaviour can be restored by giving the option --no-status.
The default recursion depth is now infinite. The old behaviour can be restored by giving the option --recursion-level=1.
The option --strict has been renamed to --extern-strict-all.
The commandline program linkchecker returns now non-zero exit value when errors were encountered. Previous versions always return a zero exit value. For scripts to ignore exit values and therefore restore the old behaviour you can append a || true at the end of the command.