Fullmetal alchemist (2003) TV series is a wonderful anime! If you like action and serious stories then it is surely for you. There is blood, there are killings, there are tragedies and adventures, mysticism and science - it's all there! If you want some brotherly love and friendship ties, revenge and forgiveness - watch this anime!
Opening and ending sequences are embellished with cool music making them a pleasure to watch.
Here I am going to show you some "mistake" which I found, but it contains a little spoiler. Scroll down at your own risk :)
I noticed one "mistake" - it was Nina's body remains on the wall. The first episode showed them like this
but the next one changed it completely showing us just a big blood stain on the wall