Question: I'm using Lubuntu 11.10. Every time I shut down I can read FAIL in red letters, but I can not read more. 

So, how to read the log messages and try to solve the problem?

Answer: 
You need to edit all the /etc/rc6.d/\* files and redirect their output to some file, which you can read later.

This redirection, will also tell you, which program `failed` and `why`.

Additionally, you have to modify the `start-stop-daemon` by removing `--quiet` parameter and adding `-v` parameter in all those files.

If you are doing so, then make sure, you will rollback all the changes all you made. Backing up the existing files before making changes will be good idea.
Like Graeme said, with ro or dismounted filesystem, killed klogd there is no way 
to write such info to a file. A solution may be using a console ( serial port ) ,
defined in bootargs. Just connect null modem cable and another PC ( tablet or 
smartphone with appropriate adapter ) and terminal emulator.