why is it important to measure weather accurately?
It really depends upon what you are doing with that data. If you are doing something that depends on the weather, it could help you predict storms, wind, and other important weather related phenomenon. In many cases like, camping, sailing, or climbing, that information could save your life.
Having an accurate database of the weather over time, can be useful information in the sciences. Climatologist use it to predict changes in the Earth's weather and climate. Ecologist correlate weather data with changes in ecosystems to look for possible cause.
If you do not, you could run into storms, dust bowls, or other examples of natural disasters