You've been asked to review it, so yes, you should absolutely point out all the errors, whether they're spelling, grammatical or technical! Not fixing it is definitely not on the table, as if it goes out to clients with those errors, you'll be asked why you didn't notice any of them.
I do realise that life isn't often ideal, and there is a worry that some managers may take offence at having loads of corrections thrown at their work. If you feel this is the case, then I'd just shoot an email along the lines of:
Hi x,
I've been reviewing the manual you sent and noticed a few spelling errors, would you like me to correct those as well as making comments on any technical issues?
You can then progress knowing that you've been told to look out for these issues as well.