On the surface, it makes sense to interact only with those individuals who have the same interests and skills as you. In reality, however, these contacts are unlikely to get you to the next level. In fact, they may view you as competition. This is not to say you shouldn't have anybody in your network like this; you should just make sure to have a more diversified contact list.
Another bad networking habit is only beginning the process when you don't have a job. You should really be working to make new contacts even when you are employed. Desperation is no way to conduct a job search, and having ready-made contacts to turn to if you become unemployed will be useful. Start developing relationships today but remember, don't ask for favors right away.
Job seekers sometimes make the mistake of choosing quantity over quality. In other words, they have hundreds of contacts, but have neglected to cultivate real relationships with most of them. It's much more effective to have a handful of really good networking contacts than to have hundreds with whom you have no connection.
Finally, you should know exactly what you want when you begin your networking. You obviously want a nonprofit job, but what kind? What position are you specifically looking to obtain? If you don't know what you are looking for, how can someone else help you?
At the end of the day, networking is what you make of it. If you put a lot of time and effort into it, you will get great results. But if you don't take it seriously and make mistakes like the ones listed above, it's not likely to help you much.