I'm also a first year, non-native English speaker PhD, but I've been doing some writing with my Master thesis adviser (native speaker of my language, not English, but very well versed in English and ~2 more languages). In any language, I often have long causal (is that the right word?) sentences, and he sometimes wouldn't agree with my style.
Even though I was the one doing most of the writing, I still feel like I can offer some useful tips. And, before the list, I support everyone arguing strategy and being careful that your actions aren't misinterpreted as disrespectful
if it's just typos (spelling), or obvious grammar ("It's advantage" vs. "Its advantage"), just correct it on your own and accompany it with an SVN comment ("Ran text through spellchecker", "Spotted and corrected few minor spelling mistakes")
If you feel like your professor has an easily-bruised ego, make it sound like not a big deal. Just some routine check-ups and tune-ups you did, nothing major you changed.
request in person meetings, or (in case it's not possible to meet in person) video-conference/phone-call meetings or at least ask the guy (nicely!) if it would be okay to collect and send your opinions and confusions on the paper via e-mail once or twice a month or so
keep track of passages and expressions that you would change. Rank them if you want, from the ones that are just plain confusing you and which you can not understand, to the ones that sound strange language-wise to the ones you just think you have a better expression for.
If you sit on that information for a few days, you'll come to terms with some of them, realize that some are really a matter of personal style, and which parts are just simply confusingly written and hard to understand.
communicate with the professor, respectfully and diplomatically expressing your concerns. Some suggestions that I would feel comfortable with.
"I'm not sure if I understood what you meant in this passage here (...). I have interpreted it as (...), is that correct?" (slip your suggestion here)
"As a non-native English speaker, I am not too familiar with this expression or weather it can be used in this context. Do you think it would be a good idea if we / I checked for an alternate expression?"
"I had a very hard time to understand this part (...). After going through it and understanding it, I have re-written it in a way that sounds clearer for me. Would you have time to go through this and offer your opinion?"
"Would you mind interpreting this couple of sentences for me? I do understand the gist of it from my practical work, but I can't seem to put the pieces in place after reading it."
this way, you're not imposing your style or writing, and it can not be misinterpreted as "I think my writing is better than yours." But, as papers are written to be understood by others, you expressing your concerns might prompt him to re-think the part of the text.
If he tries to explain on the spot, and looses himself in the explanation, that should be a clear hint even to the professor that it's not really clearly written.
There is no chance of you changing the meaning of something you misunderstood. Also, you showed that even though you would write something differently, you respect his style, reasoning and opinion. My ex-supervisor always told me, it's always okay to have an opinion of your own if you can back it up and defend it. If you can both concisely explain to each other how and why you've written a portion of text, it will be easier to reach an understanding.
always offer him the chance to do it ("we might" -- it means you) but say that you can implement the changes yourself ("or I can write the potential changes" -- it means you again).
Offering them to do it shows respect of their opinion, and offering to do it yourself shows commitment and respect of their time. Very diplomatic :)
never say you think there is a problem. Saying you have a "problem" is a sign of weakness in academia - so you definetely shouldn't accuse a professor of having one. Look through my post, go ahead: I never used the word "problem" before this paragraph. Not once.
So, shortly, I strongly advise diplomacy. But also, talking to your supervisor. If you offer your suggestions in a way that tell your professor that you value what he's written, his opinion, and his work, he shouldn't have problems doing the same with you. And if he still does have a problem with it... Don't walk. Run! (by @JeffE)