How to disable autocorrection for sudo [command] in zsh

Zsh comes with a large set of completions but a smaller set of corrections. There are many commands for which completion is useful but not correction; for example, it's useful to complete arguments to mkdir (to create directories inside existing directories) but not to correct them. The correct_all option is very harsh, as it turns on correction everywhere; unfortunately, there is no option to correct only when a set of correct inputs is supplied.

You can customize the corrections for a given command by setting the corrections tag, and customize whether to perform correction by making _correct part of the matcher-list or not. These are set with the zstyle builtin.

I looked through the .zshrc and /etc/zshrc of my systems. From experimenting, to expand /v/L/S/c to /var/log/squid/cache.log, I needed three settings:

# These two initialize the completion system,
# providing the case-sensitive expansion
autoload -U compinit
compinit
# This sets the case insensitivity
zstyle ':completion:*' matcher-list '' 'm:{[:lower:][:upper:]}={[:upper:][:lower:]}'

That last line was part of a few settings added by running compinstall. I'd suggest you run it too. compinstall doesn't add many settings, so you needn't worry about bloat.