LaTeX uses \[...\] instead of $$...$$ for displayed math equations, see: Why is \[ … \] preferable to $$ … $$?
\mathbb and environment cases are supported by package amsmath. The following works without error:
\documentclass[hyperref={pdfencoding=auto}]{beamer}
\usepackage[utf8]{inputenc}
\usepackage[croatian]{babel}
\usepackage[T1]{fontenc}
\usepackage{amsmath}
\begin{document}
\begin{frame}{Ponavljanje - područje definicije}
\section{Ponavljanje - područje definicije}
\subsection{Polinomi}
\begin{enumerate}[1.]
\item Polinomi
\end{enumerate}
\centering
\includegraphics[width=50mm]{example-image-a}
\[
D_{f} = \mathbb{R} , R_{f} = \begin{cases}
\mathbb{R} & n $ neparan$ \\
[o, + \infty > & n $ paran$
\end{cases}
\]
\end{frame}
\end{document}

BTW, TeX shows the undefined command sequence in the error message at the end of the line that starts with the line number.