1. She isn't good at everything. This may sound silly, because no one is good at everything, but what I really mean is having a friend who is honest and open about what she is good at as well as her shortcomings. No one wants to hang out with the mom whose house is always spotless AND she makes everything from scratch AND she works out every day AND... When I asked my friend if she exercises and she laughed out loud, I thought, "I really like this lady."
2. She calls you on your stuff. Having girlfriends who "yes" you may be easier to deal with, but a friend who values your relationship enough to call you out when you're being ridiculous is worth a million acquaintances.
3. She'll take your kids in a pinch, even if they have a snotty nose. I don't like it when my kids hang out with sick kids. I try not to bring my sick kids to other people's houses. In the end, the world is full of germs with various incubation times, and my kids have been infected/we have accidentally infected our friends kids. When you have a date scheduled for a month and you're about to lose your mind, the best mom friend will take your baby even with the snot.
4. She lets you do things for her. This is a tough one, since many of us women folk have a hard time accepting help. It is hard to be vulnerable! However, it is very gratifying to have a friend who lets you into her life and is appreciative rather than apologetic. If you can bring dinner over for her family when she's having a tough week at work, or help her fold the ever growing mountain of laundry, that's true friendship.
5. You can talk about your marriage/birth story/challenges with your kids. Sometimes there is an awkward stage in mom friendships, when a friendship grows past the playground chatter of milestones and local activities, and turns to more serious matters. It can be difficult to open up about the things in life that we truly struggle with. The beautiful thing that I've found is that even with moms who are very different from me in many ways, we all have these deep relationships and intense experiences in common. Everyone has challenges in her marriage, everyone has a crazy birth story, and everyone struggles with certain aspects of having children. I never want to be oversharing with every mom at the swingset, but when I have allowed myself to be open, honest, and real with my friends, our relationships always grow more fulfilling.