I really liked the manga as well and I would say it is pretty faithful to the manga in spirit. To be honest, I don't remember all the details of the early parts of the manga to tell you what exactly they may have changed here or omitted there. However, the main thing I like in this series are the characters, and they definitely embody them well. Mirika is still Mirika just like Naoya is still Naoya and everybody tends to shout everything they say just like in the manga.

I think that the show gets a lot of flak from people based on the premise/genre. But, if you liked the manga, then you would probably enjoy the show too. Just set your expectations. This isn't cinema by any means, it is a turn your brain off (just like the characters) and enjoy kind of show.