I think the problem is that both memoir and tex4ht redefines lot of standard macros. tex4ht tries hard to translate LaTeX tables to their html counterparts. In order to do that, it inserts some configurable hooks to standard macros. But it seems that memoir also changes standard table macros, in some way which is incompatible with tex4ht
This problem can be solved by writing tex4ht configuration file for memoir. In fact, it exists, but it is really basic and it doesn't contain configuration for tables. You can see it on the ctan
So what is needed at the moment is that someone who understands memoir internals and the way in which tex4ht handles tables write configurations for memoir's tables and possibly other things, which memoir redefines.
Edit
For start, you can try to include configurations for packages loaded by memoir automatically. Place this file as memoir.4ht in directory with your document:
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% memoir.4ht 2009-05-21-09:32 %
% Copyright (C) 2003--2009 Eitan M. Gurari %
% %
% This work may be distributed and/or modified under the %
% conditions of the LaTeX Project Public License, either %
% version 1.3c of this license or (at your option) any %
% later version. The latest version of this license is %
% in %
% http://www.latex-project.org/lppl.txt %
% and version 1.3c or later is part of all distributions %
% of LaTeX version 2005/12/01 or later. %
% %
% This work has the LPPL maintenance status "maintained".%
% %
% This Current Maintainer of this work %
% is Eitan M. Gurari. %
% %
% If you modify this program your changing its signature %
% with a directive of the following form will be %
% appreciated. %
% \message{signature} %
% %
% gurari@cse.ohio-state.edu %
% http://www.cse.ohio-state.edu/~gurari %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\immediate\write-1{version 2009-05-21-09:32}
\input book.4ht
\input verse.4ht
% Tables Handling
\input array.4ht
\input dcolumn.4ht
\input tabularx.4ht
\input booktabs.4ht
\let\rm\empty
\let\sf\empty
\let\tt\empty
\let\bf\empty
\let\it\empty
\def\@chapter[#1]#2{%
\gHAdvance\:mpNum by 1
\HAssign\minipageNum=\:mpNum \relax
%
{\SkipRefstepAnchor \let\addcontentsline\:gobbleIII\no@chapter[#1]{}%
\global\let\f@rtoc\f@rtoc
\global\let\f@rhdr\f@rhdr }%
\HtmlEnv \Toc:Title{#1}\:chapter{#2}}
\NewConfigure{poemline}{2}
\ifx \memgobble\:UnDef
\pend:defI\getthelinenumber{%
\let\sv:thepoemline\thepoemline
\pend:def\thepoemline{\a:poemline}%
\append:def\thepoemline{\b:poemline}}
\append:defI\getthelinenumber{\let\thepoemline\sv:thepoemline}
\else
\pend:defII\getthelinenumber{%
\let\sv:thepoemline\thepoemline
\pend:def\thepoemline{\a:poemline}%
\append:def\thepoemline{\b:poemline}}
\append:defII\getthelinenumber{\let\thepoemline\sv:thepoemline}
\fi
\Hinput{memoir}
\endinput