\hhline adds white line where no line is intended

You are specifying a final hhline fragment

\hhline{*{2}{|~}*{3}{|-}|~|}

You need

 \hhline{*{2}{|~}*{3}{|-}|~}

The "white line" is not a rule drawn over the black background it is just a lack of background, thus you need to fill it, the easiest way, as shown in the previous question is not to use ~ in the \hhline (which does exactly what you ask and does not draw any line at all) but instead use - but colour the rule using >{...} to match the cell colour.

1. If the look of black cells should be \multirow-esque, then colouring the lines black would do it. For this, I used a - instead of ~ to draw the horizontal rules for the second column;
2. Using | indicates a "vline which 'cuts' through a double (or single) hline" (according to the hhline documentation). Removing this from your \hhline specification at the end drops the "hline fragments."

3. Since you're using \vline 1.5pt as your column divisions, you might as well use

   \setlength{\arrayrulewidth}{1.5pt}
   

   to have a consistent look for your table. Otherwise you will notice little indents in your vertical rules.

Here's a MWE showcasing the above:

\documentclass[11pt]{article}
%\usepackage{color}% http://ctan.org/pkg/color
%\usepackage{multirow}% http://ctan.org/pkg/multirow
\usepackage{colortbl}% http://ctan.org/pkg/colortbl
\usepackage{hhline}% http://ctan.org/pkg/hhline

\begin{document}
% Empty table
\setlength{\arrayrulewidth}{1pt}%
\begin{tabular}{*{5}{!{\vrule width 1.5pt}p{1.5cm}}!{\vrule width 1.5pt}l}
\centering 4 &
\centering 10 &
\centering 24 &
\centering 48 &
\centering 72 &\\ \hhline{*{5}{|-}|~|}
 &  &  &  &  & Optic tectum \\ \hhline{*{2}{|~}*{3}{|-}|~|}
 &  &  &  &  & Retina \\ \hhline{*{2}{|~}*{3}{|-}|~|}
 &  &  &  &  & Myomeres \\ \hhline{*{5}{|-}|~|}
 &  &  &  &  & Arches \\ \hhline{*{5}{|-}|~|}
\end{tabular}

\bigskip

% Partically filled table
\setlength{\arrayrulewidth}{1.5pt}%
\begin{tabular}{*{5}{|p{1.5cm}}|l}
\centering 4 &
\centering 10 &
\centering 24 &
\centering 48 &
\centering 72 &\\ \hhline{*{5}{|-}|~}
 & \cellcolor{black} &  & \cellcolor{green} &  & Optic tectum \\ \hhline{|~*{4}{|-}|~}
 & \cellcolor{black} &  & \cellcolor{red} &  & Retina \\ \hhline{|~*{4}{|-}|~}
 & \cellcolor{black} &  & \cellcolor{blue} &  & Myomeres \\ \hhline{*{5}{|-}|~}
 & \cellcolor{blue} &  & \cellcolor{yellow} &  & Arches \\ \hhline{*{5}{|-}|~}
\end{tabular}

\end{document}