Better than filling these nodes with a solid color which matches the background color, is not to fill the nodes. This way, if the background color changes, the code is still correct.
To do so you only have to remove the fill=white and draw=white options for those nodes. This way, no filling nor drawing takes place.
To have little dots at the vertices of hexagon, you can use every node/.style in a scope. Also, do not use \draw for the hexagon, but \path, since the edges are drawn later.
This is my suggested code:
\documentclass{beamer}
\usepackage{tikz}
\setbeamercolor{background canvas}{bg=orange!50!white}
\begin{document}
\begin{frame}
\begin{center}
\begin{tikzpicture}[scale=0.4]
\begin{scope}[every node/.style={circle,minimum size=2pt,
inner sep=0pt, fill}]
\path node (1) [label=$v_{1,1}$] {}
-- ++(330:2.0cm) node [](2) [] {}
-- ++(270:2.0cm) node (3)
[] {}-- ++(210:2.0cm) node (4)
[] {}-- ++(150:2.0cm) node (5)
[] {}-- ++(90:2.0cm) node (6)
[] {}-- ++(30:2.0cm) node (1)
{};
\end{scope}
\path [](1) edge (2);
\path [](2) edge (3);
\path [dashed] (3) edge (4);
\path (4) edge (5);
\path (5) edge (6);
\path [](6) edge (1);
\draw (4) node[below,xshift=0mm,]{Layer 1};
\draw (1) node[below,yshift=-5mm]{$K_n$};
\end{tikzpicture}
\end{center}
\end{frame}
\end{document}

Update. Not related with your question but leveraging the opportunity, your code can be refactorized to use a loop and custom styles, to make it shorter and (imho) more readable:
\documentclass{beamer}
\usepackage{tikz}
\setbeamercolor{background canvas}{bg=orange!50!white}
\begin{document}
\begin{frame}
\begin{center}
\tikzset{
smalldot/.style={circle,minimum size=2pt, inner sep=0pt, fill}
}
\begin{tikzpicture}[scale=0.4]
\foreach \angle [count=\n from 1] in {30, 90, ..., 330}
\node[smalldot] (\n) at (\angle:2cm) {};
\draw (6) -- (1) -- (2) -- (3) -- (4) -- (5);
\draw [dashed] (5) -- (6);
\node[above] at (2) {$v_{1,1}$};
\node[below] at (5) {Layer 1};
\node at (0,0) {$K_n$};
\end{tikzpicture}
\end{center}
\end{frame}
\end{document}
draw=whitefrom the draw calls of the specific nodes? – epR8GaYuh Jan 23 '17 at 06:48