My first-grader has just started to get homework on a regular basis. As background, I always swore that I would not be doing my child's homework for him, or with him - I see it as being important for kids to take ownership of their work and responsibilities. I've seen my role as being limited to perhaps helping him figure out a concept when he is stuck, helping him make sure that the work is where it should be (until he's developed his own organizational method) and minor stuff like that. I'd rather have him send back homework with his own mistakes than done perfectly with (what I see as) over-involvement by me.
So of course, it's easy to say that in theory, but much harder to do in practice. I glanced at my DS's homework sheet to find that he made a fairly simple mistake because he rushed. I handled it not by pointing out the mistake, but by telling him that when DH and I do assignments at work, we always take the time to double-check. I asked that he take a moment to double-check (a habit I'd like him to develop early), and he caught the mistake. If he hadn't caught it, I was prepared to just have him send it in and have it marked wrong by the teacher.
I guess what I'm wondering is, does this square with what's expected in the classroom now? Is it going to be perceived as DS being held accountable or as DS being sent to school not as prepared as other kids? Do you let your kids make their own mistakes on homework; do you review it with them; do you correct it?