After enumerating the cells, I get errors. I do not have any problems when I use the bullets. So, I am sure about the table structure, but wondering why I get errors when I use numbers! Thank you in advance.

%%% document setup
\usepackage{mathptmx}%times new roman
%%to breack down line in a table
\vskip .25in
& A & B & C & D\vspace{.2cm}\\\hline
\multirow {3}{*}{{\rotatebox[origin=c]{90}{E~\cite{for example}}}} 
&\vspace{.2cm} A\vspace{.2cm} & B & \multirow{3}{*}{
\item {tttt}
\item {wwww}
& \multirow{3}{*}{
\item {iii}
&C & D &&  \\\cline{2-3}
&\pbox{1.6cm}{E} & F && \\\hline


any list -- itemize, enumerate or description used in table had to be parbox like cell, for example in p{...}. all columns in your table are such, however your list is multirow cell, which has different cell type:

\multirow{2}{*}{ ... }

which consider column formatting (p{...}) not consider column formatting but l cell (column) type. if you will replace existed multrow commands with

\multirow{2}{=}{ ... }

and have installed recent version of multirow packages, your mwe will work as expected.

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