Are dark night problems a common thing? It worries me that if I practice they might happen

As hinted to in the article, they are perhaps not a common thing. However, such issues highlight the benefits of having a teacher that can help with moving on from a place where you are experiencing difficulties.

1. It's not helpful to avoid meditation because of the view of a single source claiming there are dangers. Skillful meditation practice works with reducing fears, such articles tend to increase fears. Fear, in Buddhism, is a prominent cause of suffering

2. If you are not experiencing these "dark nights", worrying about them will do no good. If you are experiencing them (I interpret your question as you aren't), then seek help from a qualified teacher - don't run away from them, even if that should be your first inclination.

3. The benefits of Buddhist meditation are many and the popularity of meditation spreading in the West, testify to that.

4. Difficulties will certainly arise - in meditation as in life in general. Buddhism provides methods and (thousands of) techniques to deal with difficulties. Since there are so many teachings, it's usually best to have a teacher help guide you on the way.

From the article:

"the main delivery system for Buddhist meditation in America is actually medicine and science, not Buddhism."

By going to a Buddhist teacher (i.e. monastic), there may be better chances of dealing with such experiences, skilfully.

Quoting Shinzen Young from the article:

Almost everyone who gets anywhere with meditation will pass through periods of negative emotion, confusion, [and] disorientation. …The same can happen in psychotherapy and other growth modalities. I would not refer to these types of experiences as 'dark night.' I would reserve the term for a somewhat rarer phenomenon. Within the Buddhist tradition, [this] is sometimes referred to as 'falling into the Pit of the Void.' It entails an authentic and irreversible insight into Emptiness and No Self. Instead of being empowering and fulfilling … it turns into the opposite. In a sense, it's Enlightenment's Evil Twin. This is serious but still manageable through intensive … guidance under a competent teacher. In some cases, it takes months or even years to fully metabolize, but in my experience the results are almost always highly positive.

So again, don't worry, find a good teacher, and just try it. See if it's helpful. Don't make a problem of it unless it occurs.

This "Dark Night" stuff is my biggest problem with dharmaoverground.org (which is in general interesting and useful). I mentioned it here. My complaint is that it acts as a lens -- on dharmaoverground.com you'll often hear people refer to themselves as "dark night yogis" -- through which these negative aspect get focused with the result that it feeds our built-in cognitive bias to overestimate the probability of certain things occurring.

Look at Yuttadhammo's response. He's a monk and an experienced teacher, and he doesn't appear to even have heard of the thing. (Sorry Y. if I'm reading into your question). If the thing was that common, you'd think he'd have heard about it. And when the Dalai Lama met with Willoughby Britton to hear about her work (again, video link in my another thread), he seemed not to have encountered it much either.

Here's Shinzen Young again (link also in that other post): "In my entire career of teaching, ... I have encountered this in students only a few times."

When I first read about it (in Dan Ingram's book, "Mastering the Core Teachings of the Buddha", which I do recommend), I was scared too. But since broadening my reading I've decided that I'm glad to know about DN stuff, in the same way that I know about the oxygen masks in a plane. But I don't really expect to have to use either of those pieces of information.

Yes, passing through what you called "dark night" is a prerequisite for Enlightenment. The term refers to existential crisis experienced around the time of fully realizing Emptiness and the Three Marks of Existence. In Vajrayana tradition this is also referred to as the death of the ego. As Chogyam Trungpa said,

Enlightenment is ego's ultimate disappointment.

(On a separate note, I would not blindly believe anything I read on dharmaoverground.org -- that community does not seem to be grounded in genuine teaching.)