TAR 8 was filmed during the most active hurricane season in the Atlantic basin on record. and the show had to make a number of adjustments as a result. In addition to the loss of a leg in Belize which had a landfalling hurricane on the way when the teams were supposed to be there, and a second hurricane that affected the legs in Huntsville, there were two other legs that were affected as teams drove down the east coast of the U.S. from New York City to South Carolina. Then the teams rode on busses through yet another tropical cyclone on the way from South Carolina (through Atlanta, though the show never acknowledged it to Huntsville.
After they had filmed in New Orleans, Hurricane Katrina hit that area hard.
All that in just one race.
There was another season when the teams went to Siberia, and had to travel through a blizzard....on a train. Bertram mentioned that one during the pre-Race publicity although the editors spent almost no time showing it.
I'm sure there are others, but those are ones that pop up in seeing the topic.
I'll also mention that in TAR 6 we were able to use Weather Underground for information on the rain teams dealt with in Hungary during the first ever uber-leg; and for TAR 8, I was able to narrow down the date for the balloon task in the southwestern U.S. because of the specific weather conditions required for balloon flight, and the fact that of a three day range we had for the timing of the task, only one had the right conditions for a morning flight using the nearly fixed base operator weather reports from Weather Underground.
In other words, we can use weather not only to see what happens on the race, but to help date when things happened during filming.