"The sun, the moon and the stars have all changed position," they say. Even the wind, making it harder for them to make their weather predictions. The article Seen Green read did not explain what all this means long term. But one reader, Wesley Williams, who Seen Green attempted to contact on Facebook, explained that this shifting of the earth is called the "Chandler Wobble or Axial Procession." He states that is a natural phenomenon that has been noted since the days of Sir Issac Newton and as is probably the result of ocean bottom fluctuations. "Because of the tilt of the earth, and its rotational spin, there will be constant changes in this wobble." Wesley maintains.
Now, Seen green did some fact checking, and it seems not everyone agrees nor understands HOW the change in earth's axis affects the weather. For the geeks among you, feel free to follow the conversation on Earth Science Beta. Or this NOAA Paleoclimatology report on orbital dynamics. Skeptical Science even took a stab at this question.