Can PyCharm list all of Python errors in a project?

You can call Code|Inspect Code (formerly Analyze|Inspect Code, thanks to @CrackerJack9) to get all errors and warnings and ways to fix them. In result panel you can choose to see only errors (red/yellow button at the left side).


In Pycharm 2.6.3:
Code -> Inspect Code


Yes, run Analyze|Inspect Code and specify Whole project as the scope of analysis.