Import of csv file with chrome browser didn't work because file was coded in UTF16, where UTF8 was required. The UTF16 coding caused the trouble. There are characters that can't be displayed in UTF8 and this will break import or skip parts of the data.
These characters can even be invisible.
Fix: change coding of the file to UTF8 with a good text editor like Notepad++
Had trouble importing contacts.
One csv list worked, the other not.
I realized with the list that worked, that the email-address was detected automatically after the first step [upload].
With the list that didn't import, the email-address was NOT autodetected. This turned out to be the clue that lead to the solution.
Eventually I found out that both files were coded in UTF16 and that UTF8 was required.
I opened the file with LibreOffice and there appears an import dialog where it asks about coding, field delimiters etc. As the file was coded in UTF16, this was selected and the file appeared perfect. When viewed in a good text editor everything was fine too. Yet when I changed the coding to UTF8 in the LibreOffice import dialog, there where two "broken" characters right at the start. And they messed up the whole thing. They were invisible elsewhere.
To fix the file, I simply opened it with the text editor Notepad++ (freeware), changed the coding to UTF8, saved the file and anything was fine.
Import went smoothly and even the German umlauts where imported perfectly.