Unacceptable quality of writing in a letter of recommendation
I would certainly request a corrected version. Like you said, in a careful measure, I would keep the tone of the message somewhere along the lines "some minor mistakes, happens to all of us, but these little changes go a long way in credibility of the letter". In other words, don't criticize, put together a list of things you want corrected and send them to the referee. I deduce from your question that the letter was proxy-written, i.e. you haven't been told that it was the assistant who wrote it. That's why I'm recommending to contact the referee and not the assistant. However, if that is not the case, include both of them.

I can't see why someone other than an extreme ego-maniac would choose not to correct their own grammar mistakes. Even it they for whatever reason do, it's still better than just to "forget about the reference".