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: 
Easiest solution might be to try taking a video instead of a photograph. You can step through it frame-by-frame later.
Error (and other) messages are usually hidden by `plymouth` for aesthetical reasons.

Perhaps this helps: If you hit ESC during shutdown, `plymouth` shows the graphical console. Does that show you useful messages?

Apart from that, there is little you can do if the machine actually crashes because it may not be able to write the log file - whether it is buffered, or `/var/log` is already remounted read-only, depending on when the crash occurs. You could have a look at these files by executing `ls -ltr /var/log` and looking whether there is a log file that matches your shutdown date (or newer).