1) When writing his letter, he made mistakes SUCH
that nobody could understand his meaning.2 When writing his letter, he made such mistakes as you would never believe.
3) When writing his letter, he made such mistakes that you would never believe.
4) When writing his letter, he made such mistakes that you would never believe them.
5) When writing his letter, he made such mistakes that you would never believe he made them.
These are not idiomatic. "Mistakes" is a countable noun. You need to say something like "so many".