|Earth's wobble changed map|
|Change in earth's rotational speed|
|Earth's axis change and wobble|
|Earth's wobble and axis shift|
This is not a new condition. Scientists noted a wobble in the earth's axis as far back as the 1890's which at that time, it was estimated to be a 5 mile wobble. In the 1980's, the wobble was said to be 85 miles. However, current wobble estimates are from one end of the spectrum to another. We now have articles claiming the wobble is only centimeters. The wobble is at the arctic while the Antarctic is fixed. It is like a top which wobbles at the top as the spinning starts to slow down. The bottom of the top doesn't wobble. This is also called, Precession. You can look this up on wikipedia.
While they claim to use laser measurements to determine the wobble, it is impossible to get an accurate reading from the laser since the moon is also in motion and it will not follow the laser around the earth's rotation. After a few hours, the moon is out of site, thus it cannot measure an entire 24 hour period. Plus there is the rate of the wobble. This could be an alternate reason as to why the angle of the sun is off, but unlikely since the wobble would have to be in perfect sync with the rotation, otherwise the measurements would vary from day to day.
As mentioned above, the wobble is often described as a top which was spinning and is now starting to slow down. The slowing down is why the earth is currently wobbling. At the same time, the axis will also change tilt in a cyclical manner. While this can affect our weather as well... the wobble is not likely to be the cause of the sun setting 26 degrees to the north of Dallas on June 21st, the summer solstice.
It is my opinion that the wobble is also affected by the melting polar ice which shifts the weight on the earth as it melts.
Both the lunar orbit and the earth's orbit around the sun have a slight wobble as well. Any change, no matter how minor, has an effect on the weather conditions.