I am not a historian but I am Norwegian and since this series was heavily discussed when it first aired in Norway this has been quite heavily discussed in media here.

As you point out its a dramatization and not a documentary. This means certain characters need to be constructed and certain details made up as we simply do not have intimate knowledge about exactly what those people were doing at the time and in order to make the story more engaging.

Perhaps the most interesting part is the discussion between Bohr and Heisenberg. We know it happened but we do not know exactly what they discussed. We do not even know what language they spoke with each other as it could have been either german, english or even danish. There have been entire books and plays written about that particular conversation alone.

The consensus seems to be that the series is highly accurate in following the true historical events.

Most characters are also based on real people with a few notable exceptions:

• The character of Anna Friel is entirely fictional though there were certainly women in similar positions at the time so its is not impossible that such a character existed.
• The hydro plant director and wife is fictional. The actual plant director (Bjarne Eriksen) was aparently also arrested by the germans in a similar fashion to the fictional character so the story seems at least inspired him.
• And one of the last controversial aspects was how the british troops were summarily executed by the germans shortly after the crash landing. In reality, they were certainly executed but in a forest about two months later after torture and interrogations.

Some more detailed sources on what are facts and fiction in Norwegian are available in the following links. You can perhaps use google translate to read them. http://www.nrk.no/kultur/dette-er-fakta-og-dette-er-fiksjon-i-femte-episode-av-kampen-om-tungtvannet-1.12167953 http://www.aftenposten.no/fakta/innsikt/Kampen-om-tungtvannet-Hva-skjedde-i-virkeligheten-7881992.html