Telecare medical information systems (TMIS) enable healthcare delivery services. However, access of these services via public channel raises security and privacy issues. In recent years, several smart card based authentication schemes have been introduced to ensure secure and authorized communication between remote entities over the public channel for the (TMIS). We analyze the security of some of the recently proposed authentication schemes of Lin, Xie et al., Cao and Zhai, and Wu and Xu's for TMIS. Unfortunately, we identify that these schemes failed to satisfy desirable security attributes. In this article we briefly discuss four dynamic ID-based authentication schemes and demonstrate their failure to satisfy desirable security attributes. The study is aimed to demonstrate how inefficient password change phase can lead to denial of server scenario for an authorized user, and how an inefficient login phase causes the communication and computational overhead and decrease the performance of the system. Moreover, we show the vulnerability of Cao and Zhai's scheme to known session specific temporary information attack, vulnerability of Wu and Xu's scheme to off-line password guessing attack, and vulnerability of Xie et al.'s scheme to untraceable on-line password guessing attack.