The first two changes you probably noticed are the clock and screen titles.
The date and time were moved from the top of the ticker (or "lower third") to the top right area of the screen. And the titles on all screens were changed from uppercase to mixed case.
To make room for the date and time, the spacing of the letters in the titles was adjusted on several screens.
Some titles were also changed a bit:
Regional Observations became Regional Conditions
Your Local Forecast became Local Forecast
Regional Information become Almanac
Travel City Forecast became Travel Cities Forecast
Your Extended Forecast became [area name] Extended Forecast
The biggest changes were to the Extended Forecast and (now) Almanac. The Extended Forecast went from a text narrative to a three day graphical forecast.
Another thing worth noting is the addition of the area name to the Extended Forecast. These area names were custom and had to be added manually.
As a result, some viewers had their area names added quickly (ex. Atlanta in the video above on day one), while others had to wait several months (ex. Wilmington, DE getting theirs sometime in January 1992).
The other big change was to the screen previously titled "Regional Information."
Now titled "Almanac," the average high, low, and monthly precipitation were replaced with the next four moon phases.
Other than to take advantage of its graphical capabilities, I've never understood why they replaced the high, low, and precipitation data with moon phases.
I mean, aside from people interested in astronomy, is anyone tuning to The Weather Channel wondering what and when the next moon phase will be in their area?