The default output encoding used by LaTeX is OT1 and fonts in this encoding don't have precomposed accented characters. Therefore ä is first transformed into \"a which becomes \accent "7F a. Thus in the PDF file we get a set of elementary instructions for superimposing the dieresis to the a.
Load also
\usepackage[T1]{fontenc}
so the fonts used will not suffer from this problem, because they cover the glyphs used in several European languages written with the Latin alphabet. Swedish is completely covered.
\documentclass[12pt, a4paper]{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage[swedish]{babel}
\usepackage{fullpage}
\begin{document}
åäö
\end{document}
\usepackage[T1]{fontenc}– egreg Nov 13 '13 at 18:08