How to align two images side by side and to scale them automatically to use whole slide?

If vertical size do not matter, then you could use

\includegraphics[width=<X>\textwidth]{<first image>}%
\includegraphics[width=<1-X>\textwidth]{<second image>}

Here <X> denotes a number in (0,1), while <1-X> denotes its complement in the interval (0,1). Note the % to remove any space between the images. For equally-sized images, <X>=<1-X>=.5. Using only width as the scaling dimension will scale the height proportionally, maintaining the aspect ratio.

If vertical size does matter, you can also specify the height.

Just use width=0.5\textwidth instead of scale=3. The width option will scale an image to match the given width while keeping the aspect ratio.

To get a little white space between them you may use something like this.

\begin{figure}
   \includegraphics[width=0.475\textwidth]{peer}
   \hfill
   \includegraphics[width=0.475\textwidth]{peer-inconsistent}
\end{figure}

If you want to add captions to it, I suggest:

\begin{frame}{Pixelweise Segmentierung}
    \begin{figure}[ht]
        \begin{minipage}[b]{0.45\linewidth}
            \centering
            \includegraphics[width=\textwidth]{a.png}
            \caption{Label for a}
            \label{fig:a}
        \end{minipage}
        \hspace{0.5cm}
        \begin{minipage}[b]{0.45\linewidth}
            \centering
            \includegraphics[width=\textwidth]{b.png}
            \caption{Label for b}
            \label{fig:b}
        \end{minipage}
    \end{figure}
\end{frame}

Additionally, you might want to add the line

\setbeamertemplate{caption}{\raggedright\insertcaption\par}

to prevent the prefix "Figure" (source).