Respostas:
Sua pergunta pode ser expressa com mais clareza, esp. o que você quer dizer com "permissões erradas" para um diretório público?
Supondo que você deseja que os diretórios sejam 755 e os arquivos comuns sejam 644, eu faria assim:
$ find \! -perm 644 -type f -o \! -perm 755 -type d
Tudo depende do que você considera 'permissão incorreta'. O man find ajuda a definir a maneira como você pode procurar arquivos / diretórios com a permissão dada:
-perm -mode
All of the permission bits mode are set for the file. Symbolic modes are
accepted in this form, and this is usually the way in which would want to
use them. You must specify ‘u’, ‘g’ or ‘o’ if you use a symbolic mode.
See the EXAMPLES section for some illustrative examples.
-perm /mode
Any of the permission bits mode are set for the file. Symbolic modes are
accepted in this form. You must specify ‘u’, ‘g’ or ‘o’ if you use a
symbolic mode. See the EXAMPLES section for some illustrative examples.
If no permission bits in mode are set, this test matches any file (the
idea here is to be consistent with the behaviour of -perm -000).
-perm +mode
Deprecated, old way of searching for files with any of the permission
bits in mode set. You should use -perm /mode instead. Trying to use the
‘+’ syntax with symbolic modes will yield surprising results. For exam‐
ple, ‘+u+x’ is a valid symbolic mode (equivalent to +u,+x, i.e. 0111) and
will therefore not be evaluated as -perm +mode but instead as the exact
mode specifier -perm mode and so it matches files with exact permissions
0111 instead of files with any execute bit set. If you found this para‐
graph confusing, you’re not alone - just use -perm /mode. This form of
the -perm test is deprecated because the POSIX specification requires the
interpretation of a leading ‘+’ as being part of a symbolic mode, and so
we switched to using ‘/’ instead.