-- Story --
(Mild plot structure spoilers.)
First 5 chapters set up a really basic "friends get kidnapped and have to play through games designed to test their friendship" scenario. The scope of the story opens up a lot more in chapter 6, and this is when the manga starts showcasing its strengths.
Bulk of the manga involves watching the characters challenge these "Tomodachi Games". The games are very well thought out, and seeing the characters' unique approach to each of these games ensure there's never a dull moment.
-- Characters --
Like the story, the initial introduction of the main characters was very weak; they came off as very basic interpretations of their respective character types. They didn't even look or feel like a group of friends, which is pretty bad considering the premise of the series. Thankfully, the character development significantly picks up from chapter 6 onwards, and damn is the development good.
Due to their bonds constantly being tested, it's natural for the nature of their relationship to continually change. We can see exactly how the changes affect their interactions with one another, and how each successive Tomodachi Game builds upon those changes. Layers of depth are constantly being added to their relationship, and seeing the meaning and weight behind all of their interactions adds to the manga's rewarding reading experience.
Main characters aside, we also get a colourful cast of side characters. What they lack in character development is made up aplenty with strong characterisation and seamless integration into the story and setting. Whether it's for hating on an antagonist, comedy, fanservice, empathising with a character or whatever, Tomodachi Game has it all (maybe) and it does it all well (definitely). Without a doubt, the side characters also greatly contribute to the enjoyment of the manga.
(P.S. Marie is best girl.)
-- Other --
I wasn't paying much attention. Can't think of anything bad off the top of my head. Facial expressions and emotions are portrayed really well. The "sakuga" shots are great.
I read chapters 15 to 66 continually over 13 hours. This is a monthly manga.