The bizarre weather we've had across the U.S. lately is due to a phenomenon called La Niña. It can have a number of different effects on conditions, and they aren't always the same from cycle to cycle. It's a completely normal aspect of our planet, even if the weather it causes can seem unusual.

http://www.accuweather.com/blogs/news/story/44401/year-of-extremes-strongest-la.asp

Although it says there's only a 10% possibility, could that.. be wrong?

Of course, it could be 5% or… 2%. But could be 20% or 30%… nothing is for sure, but the probability of a strong earthquake within the next year is very low. Do you live near New Madrid Seismic Zone? Illinois, Indiana, Missouri, Arkansas, Kentucky, Tennessee or Mississippi?

there's been crazy weather. Referring that this could possibly be the "quiet before the storm"….

Sometimes the weather gets crazy, it's normal. The weather doesn't follow a pattern.

There have been many speculations, and people claiming that the area around New Madrid is acting a bit strange.

No, it's not. Since 1974 (when they installed instruments in New Madrid), more than 4000 earthquakes have been recorded, with an average of one earthquake per year is large enough to be felt.¹

Is there any way to tell if there is any signs we can look for to determine if "the big one" is coming - if it is..?

In 1811-1812 many strong earthquakes happened in New Madrid (~7.2-8.2, 7.0-8.0 and 7.4-8.6), with hundreds of aftershocks. USGS is pretty concerned with the possibility of a earthquake like 1811-1812, within the next 50 years, but the probability is pretty small (10%).

¹. New Madrid Seismic Zone - Wikipedia.org

and people claiming that the area around New Madrid is acting a bit strange.

What people? I've seen a lot of people on this board and in other places getting hysterical over earthquakes in general, but I haven't heard anything in particular about New Madrid. Since I live nearby, you'd think I would have if that were true, never mind that I would probably notice firsthand.

There have been massive swarms of earthquakes in Arkansas

Earthquakes in Arkansas aren't unusual, especially around the New Madrid region. The recent quakes have been around a small town called Guy, which is in the north-central part of the state, some distance from New Madrid, most of them very small. The tremors don't appear to have anything to do with any fault, but rather seem related to salt water disposal wells in the area. Investigation is ongoing, but this is hardly a concern aside from bothering the people in the area who aren't used to this sort of thing.

FWIW, I live in Arkansas, and it's not a big deal here except around that one town.

There is nothing unusual about the earthquakes going on. The reason there seem to be more is because they are recorded more often nowadays. I don't know much about the New Madrid Fault (I will let someone else answer that) but Yellow Stone isn't expected to erupt until a long time.

I've recently been reading a few news articles, as well as hanging around forums that include great detail about New Madrid Fault Line. I'm not quite sure you all could answer this, or if anyone could even answer this regardless of the amount of knowledge; There have been massive swarms of earthquakes in Arkansas, I'm just worried if that will trigger the New Madrid Fault to let out "the big one" or possibly even a massive Yellowstone eruption? Apparently the amount of earthquakes was hardly even recognizable, and now there's like 500 coming out of nowhere! Could you tell me if this is a sign of anything..? I can't stop panicking.