Let me start off by saying that I think 1864 is a beautifully filmed series with several solid performances and a lot of work put into creating the scenery, props and costuming. That being said, it's saddled with a pretty lukewarm script. There were lots of places Bornedal could have gone with this piece of history, and at times one is confused as to why he made some of the choices he did. One of the most common complaints is the present-day connection, which does feel unnecessary at times, but what's far worse are the absolutely out-of-the-blue supernatural elements which pop up toward the middle of the series and add nothing to the story but a thoroughly shattered suspense of disbelief. Beyond that bit, I found the series to be reasonably historical. Not a documentary, mind you, but as faithful as could be reasonably expected. The other problem with the series is that it occasionally lays on the melodrama too thick, sometimes almost comically so.
TL;DR- Despite the the writing problems, I found myself captivated by this shiny, sometimes stupid period drama. (also, ep. 7 contains one of the most epic battle sequences I've seen in a long time, so there's that.)
**If you're reading this in another country, you ought to know that many ratings and reviews of this series are highly politically charged. Some liberals hate it outright because it received so much public funding, and the Danish Peoples Party hates it for its (justifiably) negative depiction of extreme nationalism and its consequences.