You can often diagnose a problem with MultiBit by looking at the Messages window by selecting the 'View | Messages' menu option.
For a more detailed description of what has happened with MultiBit there are two log files to look at. These are in the 'log' directory in your application data directory. The two files are:
MultiBit stores user specific data such as logs and the default multibit.wallet in a "user application data directory". This directory can be worked out as follows:
1) See if there is a multibit.properties in MultiBit's current working directory. If there is, use this directory as the application data directory. This is for backwards compatibility and for running everything from a USB drive.
2) Otherwise set the user application data directory as follows:
<"APPDATA" environment setting>/MultiBit e.g. C:/Documents and Settings/Administrator/Application Data/MultiBit
<"user.home" system property>/Library/Application Support/MultiBit e.g. /Users/jim/Library/Application Support/MultiBit
<"user.home" system property>/MultiBit e.g. /Users/jim/MultiBit