I can't really make a minimal working example who shows the problem, because the problem just are there sometimes. But here is the code used:
\documentclass[twocolumn, a4, 12pt]{article}
\usepackage[utf8]{inputenc}
\usepackage[danish]{babel}
\begin{document}
\end{document}
Sometimes the hyphenation splits the word incorrectly in the danish version. Like "marmo-rgade" or "kal-ksten". That is one problem. The other problem is that it sometimes don't split the word at all, so the word sometimes reaches into another column (and lay over another word).
I thought danish babel should solve this problem? Am I the only one with this problem and do anyone know how to solve it? I've solved it earlier by chaging the sentence - but always to do that in a long document is too hard.
Thank you very much in advance. Kind regards!

mar-mor-ga-deandkal-k-sten(the second word seems indeed dubious, but I don't know Danish). You should also load\usepackage[T1]{fontenc}in order to hyphenate words containing accented letters such as ä. – egreg Oct 07 '15 at 20:42\showhyphens{...}; the report will be on your screen and in the log, but not typeset. if something really isn't hyphenating where it ought to, you can fix it in a\hyphenation{...}directive, or use a "discretionary hyphen",\-. – barbara beeton Oct 07 '15 at 20:51input{hyph-dan.tex}. For US-English there is a neat precompiled list that can be called with\input{ushyphex.tex}but for other languages you are on your own. – Florian Oct 11 '15 at 10:14