Season One of Sailor Moon encompasses the best and worst of the entire Sailor Moon franchise.
Sailor Moon introduces us to Usagi at her most comedic: she is not only the heroine but the comic relief of her own show. Over the course of the season we are introduced to Luna, Sailor Mercury, Sailor Mars, Sailor Jupiter and finally Sailor Venus and Artemis.
As others have mentioned, it is the characters, their relationships with one another which really holds the show together. Other shoujo such as Card Captor Sakura, handled the monster of the week nature in a more fun and varied way, but few anime have handled girls in all their complexities and silliness as well as Sailor Moon has, before or since.
Sailor Moon is about girl power and while the anime emphasis may not be as strong as the manga, it's definitely still there. The girls have complex characters; it's not about defining them by one characteristic, the dumb blond or the tough tomboy (as American cartoons often do) but by letting the girls be multi-faceted, even paradoxical; the tomboy who is boy crazy and romantic, the dumb blond who is athletic and dedicated to her mission. Sailor Moon saves Tuxedo Kamen's butt for every time he saves her, more so as the season goes on. And all of the girls change and grow through the challenges they face.
With such a large amount of characters and cool-looking villains, Sailor Moon is also one of the most lastingly popular series for fanart and fanfiction. Someone or some relationship is bound to catch your interest and play you right along. Which is all part of the fun. Planets, stones, mythology, past lives, romances. This series has so much to play with and it all adds to the appeal.
The monster of the week aspect forms the larger part of the series, which is hit and miss. Some episodes delve into character development, exploring the girls' past and seeing why they are who they are. Others are primarily comedic in nature, such as the episode with the cat who falls in love with Luna, mocking Tuxedo Mask's and Sailor Moon's relationship (everyone has made fun of Tuxedo Mask, but Sailor Moon did it first). Others are boring, silly and a bother to sit through.
The best episodes are the first handful and the second half of the anime, I think. Once the Nephrite arc ends, the series picks up. Kunzite and Zoicite are threatening, the monster of the week format is shaken up and things get serious. At this point, even the filler episodes can be grim. And, of course, as with any season of Sailor Moon, the finale delivers in big ways.
There's no doubt the budget for this anime was less than to be desired; being a shoujo, that was its inevitable fate. Thus the animation and sound effects are sub-par. However, the voice acting it strong and a lot of heart went into this show. And following seasons pick up, the animation improves and the soundtrack simply gets better and better.
I think the main question is whether Sailor Moon is riding entirely on nostalgia, or if it still holds up today. Not having watched Sailor Moon as a child and watching the first season for the first time in my life at 23, my opinion is that, while flawed, it is still a worthy watch. There's history in the making in this show. Skip the filler if you want and watch the core plot episodes. They're worth it.