Sometimes, people don't see the flaws in both their child and their parenting because they are needing to ignore it. Sometimes, parents have such strong feelings about how they were parented. Not wanting to repeat those mistakes, they err on the side of becoming inappropriately permissive. Some are afraid to be authoratative because they have confused it with being an authoratarian or abusive parent. Some parents are afraid of their child not liking them, and so they choose to overlook the child's negative actions because disciplining feels emotionally dangerous to them.
In any case, it's likely that somewhere deep down, your friend knows that this isn't in either she or her son's best interest, but may be terrified at addressing this. This may be an extremely conflicting experience for her, too.
If you want to continue the friendship, just head out without the kids. I have to admit, I don't know anyone who parents exactly the same way I do, but I do have friends who are more involved during playdates than others I've seen. I'm also confident in stepping in and correcting things if the parent doesn't seem responsive. This is usually done as a group problem-solving moment, instead of singling their child out.
I'd say, maybe your friend has a lot of good qualities, but this is her challenge for right now. Mothers who have to address these deep-seated issues in their lives need friendship and support, so as they say, don't throw the baby out with the bathwater. Or rather, don't throw out the girlfriend because of this disappointing difference in parenting styles. Unless, of course, there was nothing else in common... and if you aren't interested in staying friends with her, don't make it about her. This is your discomfort with who she is and what she's dealing with right now. If you aren't going to stand by her, don't tell her what you told us about the parenting. She'll only feel sucker-punched and only feel worse about herself.