We had a very interesting issue in a project where the client was reporting an error in a screen that had hundreds of input fields but the client was not able to give us reproducible steps for the error. All that the client said was that the error was coming when a certain subset of values were selected in the input fields and the subset did not remain the same each time. In this case without reproducible steps it was virtually impossible to solve the problem.
After a bit of thought, what we decided to do was to use Snagit video screen capture and record the screens of a group of developers using the screen causing the error extensively. Once we had this video we played it back and identified the points where the error was occurring and we could then rewind and take a snapshot of the screen just before the error occurred and also write down the steps that led to the data that caused the error. With this information we were able to identify a pattern that was causing the error and solved the problem easily.
Interesting problems always makes you think out of the box. If you have some experiences similar to these please leave them in the comments section.