DNN 4.7.01
Browser: Firefox 2.x
Attached Custom HTML skin file, CSS file,
Note - container skin = dnn blue (to simplify)

Skins don't get more simple than this.  I have attempted to clean up many of the HTML tags and move them to the CSS file.  In doing so, I seemed to have made the 'Links' module content not able to "center" as it would before I started to make changes.

The panes in question are the RightPane and LeftPane.  Both contain different Links modules with a single entry each.

The HTML for this section includes:
< table cellpadding="0" cellspacing="0" width="100%" border="0" >
    < tr >
        < td class="contentpane" id="ContentPane" runat="server" align="center" colspan="2" >< /td >
    < /tr >
    < tr >
        < td align="center" class="leftpane" id="LeftPane" runat="server" >< /td >
        < td align="center" class="rightpane" id="RightPane" runat="server" >< /td >
    < /tr >
< /table >

The CSS for these classes include:

As suggested, I changed the module align settings to 'Not Specified' under the module > Settings > Page Settings > Alignment.

In Internet Explorer - no worries; Firefox 2.x - worries.

Interestingly, when in Edit mode the links text aligns center as desired, but in view mode it aligns left. When I view source < a class="Normal"... > is assigned to the actual link anchor for the entry.  See below:

< !-- End_Module_392 -- >
< /div >< /span >
< /td >

                            < /tr >
                            < tr >
                                < td id="dnn_LeftPane" class="leftpane" align="center" >< a name="377" >< /a >< span id="dnn_ctr377_ContentPane" >< !-- Start_Module_377 -- >< div id="dnn_ctr377_ModuleContent" >
 < div id="dnn_ctr377_Links_pnlList" >

  
    < table id="dnn_ctr377_Links_lstLinks" cellspacing="0" cellpadding="0" summary="Links Design Table" border="0" style="border-collapse:collapse;" >
   < tr >
    < td valign="top" >
            < table border="0" cellpadding="4" cellspacing="0" >
                < tr >
                    < td nowrap >
                       
                       
                        < a class="Normal" href="/DNN4701_02/LinkClick.aspx?link=65&tabid=58&mid=377" target="_self" >Enter Site< /a >
                         

                       
                    < /td >
                < /tr >
                < tr >
                    < td >
                       
                    < /td >
                < /tr >
            < /table >
        < /td >
   < /tr >

  < /table >

 < /div >

< !-- End_Module_377 -- >
< /div >< /span >
< /td >

                                < td id="dnn_RightPane" class="rightpane" align="center" >< a name="378" >< /a >< span id="dnn_ctr378_ContentPane" >< !-- Start_Module_378 -- >< div id="dnn_ctr378_ModuleContent" >
 < div id="dnn_ctr378_Links_pnlList" >
  
    < table id="dnn_ctr378_Links_lstLinks" cellspacing="0" cellpadding="0" summary="Links Design Table" border="0" style="border-collapse:collapse;" >
   < tr >

    < td valign="top" >
            < table border="0" cellpadding="4" cellspacing="0" >
                < tr >
                    < td nowrap >
                       
                       
                        < a class="Normal" href="/DNN4701_02/LinkClick.aspx?link=61&tabid=58&mid=378" target="_self" >Enter Blog< /a >
                         
                       
                    < /td >
                < /tr >

                < tr >
                    < td >
                       
                    < /td >
                < /tr >
            < /table >
        < /td >
   < /tr >
  < /table >

 < /div >

< !-- End_Module_378 -- >