The bzexe command in bzip2 1.0.5 and earlier generates compressed executables that do not properly handle temporary files during extraction, which allows local users to execute arbitrary code by precreating a temporary directory.
Race condition in bzip2 1.0.2 and earlier allows local users to modify permissions of arbitrary files via a hard link attack on a file while it is being decompressed, whose permissions are changed by bzip2 after the decompression is complete.