Mail() takes an optional fourth argument for attachments. It should be possible to save the log window content as a textfile and then attach it to the email. Another possibility is to add the Log output at the end of the message. Below is an expanded version of the above script that enables the user to describe the problem in her own words and the current log content is added below automatically. I tried on Windows 7 and JMP 9. The Mail ended up in Outlook's outbox and appeared as intended.
New Window( "test",
Lineup Box(
2,
Text Box( "Follow this link" ),
bb1 = Button Box( "http://www.jmp.com/", Web( "http://www.jmp.com/" ), Underline Style( 1 ) ),
Text Box( "Send mail to" ),
bb2 = Button Box( "test@example.com",
New Window( "Message text",
<<modal,
message = Text Edit Box( "Write mail message", <<set width( 200 ), <<setnlines( 10 ) ),
H List Box(
Button Box( "Ok",
content = message << get text || "\!r\!rLog Window\!r" || (Window( "Log" )[1] << show window( 1 ) << get text)
),
Button Box( "Cancel" )
)
);
subject = "Problem with your application";
Mail( "test@example.com", subject, content )
),
bb2 << Underline Style( 1 )
)
);