One thing I noticed was that it skipped entirely one of the most important parts of the Death Note series. It is where we really get to know Mello, and also we say goodbye to one of the characters of the series. There were other scenes that they highlighted that could have been skipped instead of that one. Due to this, we really don't get an understanding of one of the two that succeed L. We see a lot of Near, but nothing on Mello, which I thought was kind of not a good approach.
The movie added an extra scene at the end, which I thought was great. I always wondered the reaction of the characters at the ending, and I finally got it. The rest of it was very similar to the series.
Overall, they did a great job picking out the most important scenes for a new viewer to understand what was going on (minus the scene I discussed above), so definitely pick it up.