How to debug production setup for java?

How to debug production setup for java?

I am currently working on a web-app. Basically deployed as .war file on
production enviornment. The server is tomcat7. Since the code is written
in java. There are ocassional log statements on server side. If I am given
an issue to resolve, I do not have a duplicate data-set / subset of data ,
as like production. So the problem that I face, is replicating the
scenario , in case of testing.
Since this is production enviornment, attaching a remote debugger , would
mean that the functionality would halt/ when I am stepping through break
points, So I am not able to debug remotely.
so, currently, the only visiblity I have with regards to the behavior of
the system is, The code base, and the log statements in code.
How Do you suggest I debug the server side code without restarting the
application.
Any insight in this matter would be appreciated.
Thank you.