I'd like to talk to a peer at work about their language fluency. They're bilingual, and I've noticed repeated similar grammar mistakes in communications with customers. How can I bring this up in a non-offensive way so that they can learn? I feel that because their role in the company is customer facing it's important to show more fluency to avoid reflecting poorly on the group as a whole.
This one really depends on your relationship with the person.
If you two are close - you may be able to say "hey, I noticed you always do... " and offer an informal suggestion. However, if you really don't know how the other person would respond, then that's a good indicator that you aren't close enough for this approach.
So - if you're not a close professional friend of the person in question, I strongly recommend asking your manager. How your company wants to represent itself is a company decision, and corrections to the "voice" of the company should really come from above, particularly if there's a repeated and habitual error. Keep in mind that some folks are very sensitive about their language fluency, and having a correction from a coworker that comes unasked for could feel like an attack in some circumstances. You don't really know what guidance has been shared between this person and their manager - if you go through your own management and ask, you'll be part of the standard feedback stream.
I'd love to be able to say that correcting flawed grammar is as easy as telling someone their fly is down (something you'd do ASAP, and would forget about just as quickly), but it isn't.
If, however, your manager simply shrugs and says "tell him" - do it quickly, clearly, privately and with a specific example of the wrong way and the right way of the particular error. And be sure it IS an error by checking out the current rules for expression.