A 103 episode anime, that's not a short series, and it would take some time to watch. It started off all well and great, following faithfully to the manga, but then about ten episodes in, you're bombarded with filler. And it's not just one or two episodes of filler, it's like, a whole solid block of filler episode after filler episode, to the point where you would expect you would never see an episode that is based off the manga again. Turns out that about 30 episodes out of 51 (the first 'season') are filler. Now, some serve to flesh out the back story, which, most of the time, works, but the rest are pointless events. They were actually enjoyable to watch the first couple of times, but when you eventually realize that the next episode is not going to advance the story, you lose interest, really quick. I guess one good note was that a lot of other minor characters in the manga gets more screen time here. Overall, the first season adapts the first five volumes of the manga... which the second season (52 episodes) adapts the next eleven volumes... a big difference there (I guess they couldn't work in any more additional stories in the second season without breaking the pace).
So, once you got through the tedious first season, the fun starts, and it got really good. At times, when I read the manga, I couldn't tell what the hell was going on, now with colour and cleaner animation, I could see what was originally intended by the author. The anime also seemed to explain things slightly clearer. Of course, there's also the awesomeness of seeing your favourite characters in animation. I really enjoyed the anime at this point. However, there are still some negatives, it wasn't so bad in the manga, but it seemed that characters (particularly Lenalee and Miranda) seemed to cry a lot more here, to the point of annoying-ness. I loved the way they kept the jokes and gags here, coz they worked so well, and the fact that they managed to put in a few more original ones that they made up, and that it didn't seem out of place, was great. The ending was a bit weird, but understandable considering that the manga hasn't finished yet. I mean, they included all these other small things that foreshadow what would happen later. Considering that they had to end it somewhere, I think that they chose a good point and it was done well enough. The voice acting was top notch (well, the Japanese ones were, I didn't really watch the dubbed version, and I doubt I will like them after watching the Japanese ones). There were many scenes where you could hear so much emotions in the voices, conveying the meaning of their words, the tone, it made it so much more engaging. The music in general suited the series, but some of the theme songs wasn't that great.
Overall, the story interesting and keeps you sucked in, while the animation got progressively better, and the fact that there are some minor things that they slowly built up during the story (like Allen's voice progressively getting deeper as the series went, something you won't notice unless you suddenly watch one of the earlier episodes and compare) makes this a great anime to watch.