One additional piece of information:

When I do dump out the MethodBase TargetSite, I can get the input
parameters of the Parse() function, especially the first paremeter,
"string s".  I tried to get the actual value of the parameter "s"
passed into this Parse() function, but have not yet been successful.

Do you think that this approach will eventually yield the value of the
bad data, or is there some totally different approach?

Thanks.

There really isn't any way to do that.  You have to be aware of where
the exception was thrown, and the string that was passed to whatever method
threw it.