I recently came across a simple but nasty bug.
I had a list and I wanted to find the smallest member in it. I used Python's built-in min().
Everything worked great until in some strange scenario the list was empty (due to strange user input I could not have anticipated). My application crashed with a ValueError (BTW - not documented in the official docs).
I have very extensive unit tests and I regularly check coverage to avoid surprises like this. I also use Pylint (everything is integrated in PyDev) and I never ignore warnings, yet I failed to catch this bug before my users did.
Is there anything I can change in my methodology to avoid these kind of runtime errors?
 (which would have been caught at compile time in Java / C#?).
I'm looking for something more than wrapping my code with a big try-except. What else can I do? How many other build in Python functions are hiding nasty surprises like this???
Even in Java/C#, a class of exceptions the RuntimeError are unchecked and will not be detected by the compiler (that's why they're called RuntimeError not CompileError).
In python, certain exceptions such as KeyboardInterrupt are particularly hairy since it can be raised practically at any arbitrary point in the program.

I'm looking for something more than wrapping my code with a big try-except. 

Anything but that please. It is much better to let exceptions get to user and halt the program rather than letting error pass around silently (Zen of Python). 
Unlike Java, Python does not require all Exceptions to be caught because requiring all Exceptions to be caught makes it too easy for programmers to ignore the Exception (by writing blank exception handler).
Just relax, let the error halt; let the user report it to you, so you can fix it. The other alternative is you stepping into a debugger for forty-two hours because customer's data is getting corrupted everywhere due to a blank mandatory exception handler.
So, what you should change in your methodology is thinking that exception is bad; they're not pretty, but they're better than the alternatives.
Python Pre-testing for exceptions when coverage fails