I want to do topology check using Python, but I don't know whether ArcPy can realize the function in error inspector.
Can I call error inspector and get the error records (something like attribute table) using Python (when ArcMap is open)?
You can export the errors using export topology errors geoprocessing tool http://resources.arcgis.com/en/help/main/10.1/index.html#//00170000015w000000 this will give you the same results as the error inspector.