I try to give a variant to David Carslisle answer on question. To better see obtained results I use preview package. I was surprised, that I obtain different result in comparison when I not use it! My MWE is:
\documentclass[11pt]{article}
\usepackage{array,calc,paralist}%enumitem
%\usepackage[active,floats,tightpage]{preview}
%\setlength\PreviewBorder{1em}
%---------------------------------------------------------------%
\begin{document}
\begin{table*}
\begin{tabular}{*{4}{>{\centering}m{0.8in}}
>{\centering}m{01.5in}
>{\centering\arraybackslash}m{01.5in}}
\hline
\bfseries Heading 1
& \bfseries Heading 2
& \bfseries Heading 3
& \bfseries Heading 4
& \bfseries Heading Heading Heading 5
& \bfseries Heading Heading Heading 6 \\
\hline
text & text & text & text &
\multicolumn{2}{@{}p{3in+2\tabcolsep}@{}}{
\begin{tabular}{>{\centering}p{1.5in} >{\centering\arraybackslash}p{1.5in}}%{p{1.5in}p{1.5in}}
\begin{compactitem}[\textbullet]
\item text text text text tex text text text text text text text
\end{compactitem}
& \begin{compactitem}[\textbullet]
\item text text text text text text text text
\item text text text text text text text text
\end{compactitem}
\end{tabular}\vspace*{-1ex}} \\
\hline
\end{tabular}
\end{table*}
\end{document}
With use of preview package i receive:

Without preview package the columns 5 and 6 are aligned on the top. Do I miss some option in preview package or is this some bug? As I understand preview, it should not influence on content of tables, pictures and math.