>I read that as: if you're not prepared to get the details right when you're applying for the job why should I expect you'll get the details right when you're on the job?

You shouldn't. Nobody gets everything right the first time (why do you think we have bug systems) and it would be a waste of company resources to reread every email for every grammatical error, especially when they don't actually cause the recipient to misunderstand the intended point.

The same goes for who/whom, its/it's, weather/whether, phrases such as "in a timely manor", etc.

Perfect grammar is like bug free programs: desirable in theory but too expensive and impractical in reality.