There would be always unknown traffic situations for self-driving cars in public road testings. These unknown traffic situations would be essential and critical in reinforcing self-driving/autonomy systems. The safety and reliability of self-driving cars can be improved by continuously accumulating the experiences on public roads. The ITRI MMSL Self-Driving Cars Group obtained the first test license plate on September 2019 and our public road testing and verification was kicked off on October 2019. This article describes public road situations which are not designed or encountered in private roads such as on ITRI campus and in Taiwan Car Lab, and the proposed approaches to tackle these new and challenging situations.