I tend not to have either of these boxes checked. The "allow space between" I
only ever use for aesthetic reasons and only if the client wants it. I never
use "auto resize" as this only resizes horizontally which negates any attempt
to format the table nicely.

Dragging the cell horizontal border will jump to a grid that is "built-in"
to Word and is independant to the Grid function under the Drawing menu. Using
the Alt-drag will allow non-jumping adjustments of the borders. This is very
useful but may not fully solve your problem as this function does not ensure
that the borders "connect together" in alignment. Using the grid jump to get
the boders to connect is sometimes the only way to get the "little
so-and-so's" to behave, ie move one border to a jump position, then move the
one below to the same jump position, then move them together back to where
you want them.

When you did all the format and spacing checks did you also check that the
cell vertical alignment and internal margins are the same for the whole
table? This can be check under Table, Table Properties, Cell, check that
there is one of the Vertical alignment boxes selected, if not it means that
not all of the cells are in the same alignment. The Options button here will
show if all the cells in the table have the same internal margins, if any of
the four selection boxes is not populated, again this indicates that all the
cells are not the same. FYI the "Same as the whole table" tick box is
controled by the settings in the Table, Table Properties, Table tab, Options
dialog.

It may get to the point where you may want to start from a clean slate with
this table. You could select the whole table, then use the Table to Text, Tab
sperators, then convert back to a table. At least it will be a clean starting
point for you.
Lets hope you don't have to resort to this. :-)

Hope this helps
DeanH