In builtin.c in zsh before 5.4, when sh compatibility mode is used, there is a NULL pointer dereference during processing of the cd command with no argument if HOME is not set.

In utils.c in zsh before 5.0.6, there is a buffer overflow when scanning very long directory paths for symbolic links.

zsh before 5.0.7 allows evaluation of the initial values of integer variables imported from the environment (instead of treating them as literal numbers). That could allow local privilege escalation, under some specific and atypical conditions where zsh is being invoked in privilege-elevation contexts when the environment has not been properly sanitized, such as when zsh is invoked by sudo on systems where "env_reset" has been disabled.