Monster could really have been a good show, but like so many works it tried to put too much stuff in one packet to really deliver anything.
The premise was very interesting, and if compressed into 20-30 episodes could have made a great series. However, it went the another way, putting Tenma through many many sidequests that had nothing to do with the main plot, and the wangst resulting all his encounters had not much to do with his character's development. In classical terms, we would call these 'fillers'.
If these were quickly over their existence would not ruin the overall enjoyment. However, they are treated as equally important with the main story, and the pacing which is on par with The Bold and the Beautiful totally killed the enjoyment. It's just frustrating when you'd want to see where the story twists next and nothing happens in the time of 3-10 episodes.