Unacceptable quality of writing in a letter of recommendation I have received a letter of recommendation which clearly has been written by my referee's assistant, rather than himself. That in itself wouldn't be a problem if it didn't contain phrases such as what's more... and like event study etc.

What should I do about this? Do I just forget about the reference? Do I very carefully suggest to the assistant to make some minor changes (this letter is based on a previous draft I was asked to submit)?

It may also be worth noting that the referee is the first supervisor for my thesis and I do not want to seem ungrateful by requesting changes to my letter of recommendation.

It seems to me that the use of the phrase what's more in a letter of recommendation is per se unacceptable, but my native language is German, so any comments by native speakers of English in this regard is appreciated.
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".