documentclass{beamer}
usetheme{Dresden}
begin{document}
begin{frame}{Problem}
  begin{itemize}
     item
     begin{columns}
        column{.7linewidth}
        Here I want some text with an image to the right, all in the same item
        column{.3linewidth}
        rule{.2linewidth}{.2linewidth}
     end{columns}
     item Some more text here that is long enough to continue bellow the image
 end{itemize}
end{frame}
end{document}

documentclass{beamer}
usetheme{Dresden}

begin{document}
    begin{frame}{Solution}
        begin{columns}
            column{.65linewidth}
            begin{itemize}
                item Here I want some text with an image to the right, all in the same item
            end{itemize}
            column{.25linewidth}
            rule{.2linewidth}{.2linewidth}
        end{columns}
        begin{itemize}
            item Some more text here that is long enough to continue bellow the image
        end{itemize}
    end{frame}
end{document}

documentclass{beamer}
usetheme{Dresden}

begin{document}
    begin{frame}{Solution}
        begin{columns}[onlytextwidth] %<---
            column{.7textwidth} %<---
            begin{itemize}
                item Here I want some text with an image to the right, all in the same item
            end{itemize}
            column{.3textwidth} %<---
            rule{.2linewidth}{.2linewidth}
        end{columns}
        begin{itemize}
            item Some more text here that is long enough to continue bellow the image
        end{itemize}
    end{frame}
end{document}

documentclass{beamer}
usetheme{Dresden}
begin{document}
begin{frame}{Problem}
  begin{itemize}
     item
     begin{minipage}[t]{0.7linewidth}
        Here I want some text with an image to the right, all in the same item
     end{minipage}%
     begin{minipage}{.3linewidth}
        centering
        rule{.2linewidth}{.2linewidth}
     end{minipage}
     item Some more text here that is long enough to continue bellow the image
 end{itemize}
end{frame}
end{document}