According to Wikipedia (https://en.wikipedia.org/wiki/List_of_The_Mary_Tyler_Moore_Show_episodes), the production code in the corner lists a number but they don't seem to go in order. Is that number the order in which they were shot and then aired in a different order?

As for as the first season, was that second episode not the second one shot?

That happened with lots of shows in the 70's. The network decides which eps to air which happened with Welcome Back Kotter and Three;s company. Its done so viewers dont get confused by a certain situation