I feel like a good number of moments from Season 1 wouldn't be suitable for kids.
For example, in the Peter Ustinov episode, there's "You Do Something To Me". I understand that a lot of kids back then were terribly frightened of it, and I know that I would be too.
Second, there's the Vincent Price episode. Considering that this episode was meant to be...you know, themed around scary-type moments. "I've Got You Under My Skin" would really make kids feel unsettled, since it involves one character eating another character- the same applies to the Discussion Panel, and especially the Muppet Newsflash skit.
Depending on what kind of person the child would be like (meaning if they're one who easily gets scared of things they see on TV/movies), I personally would not not recommend showing them the "Gonzo Presents Muppet Weird Stuff" video. I borrowed it from Tower Video (anybody out there remember that place?) once when I was in first grade, thinking that it would be literally all about Gonzo, since he was my favorite Muppet Show character. However, I was partially wrong- the fact that he was presenting a bunch of weird-type moments from The Muppet Show didn't occur to me, so I was treated to not only moments revolving around Gonzo, but also a lot of other weird/eerie material that really made me feel uncomfortable, especially "I've Got You Under My Skin".
But, in general, this is all just my personal input.