I love the save system in MM, I think it is very unique. It forces you to prioritize, and it reflects reality in forcing you to realize that you can't do everything, that you have to make decisions and that said decisions might not always end up with the most effective results. It really makes MM stand out in the Zelda series and that is another reason I enjoy the save system.
I think the best part of the save system in MM was that it let the NPCs appear to have lives more real than the lives of the NPCs in Other Zelda games. They walked around and, because they were reliving the same three days it was believable that they would do the exact same things at the exact same times over those three days. (Unless you interfere in their lives, of course.) It made the NPCs interesting, it was fun to experiment with their schedules. And fortunately, in MM there are tons of sidequests to choose from, making experimenting with the NPC time schedules more rewarding.
Then of course, there is the issue of running out of time while in a dungeon, or fighing a boss. I don't recall actually running out of time on my first playthrough. (I did it on purpose just to see what would happen once or twice.) This is because I learned that you could slow down time by playing the Song of Time backwards, it made things much easier to organize and manage. There were times where I missed the deadlines for certain sidequests though, or came close to running out of time.
Overall, I think the save system in MM allowed for greater depth in NPCs than any Zelda before it, and I think that it is one of the defining features of MM. It simply wouldn't be the same without it. I can't help but love the save system in MM, it's to interesting for me to not enjoy it.