No one can say the exact date of the anniversary, because The Muppet Show was syndicated to different stations across the country -- which means that they could air it any time during the week that they wanted.
The first Muppet Show was made available the first full week of October 1976, from what I've heard. It would have been available Mon., Oct. 4. However, many stations aired it on Saturdays, so in a lot of the areas the first episode would have aired on Oct. 9, 1976 -- which is ultra-cool, because I was turning 2 years old that very day.
Technically speaking, the 25th anniversary should have been in 2001. But the Henson company wasn't able to get everything moving quickly enough for that, so they made it the INAGURAL year extending into the next (2001-02). It basically started with MF in Dec. 2001 and ended with the NBC movie in Nov. 2002.
Hope that helped.