> > emacs -Q
> > M-x customize-face font-lock-comment-delimiter-face
> > Delete the text in the Face: field.
> > Type c in that field.
> > M-TAB ; you see the completions for `c'
> 
> Indeed, I see completions starting with "c".

I was mistaken saying that.  See below.

> > Type u in that field, so you have `cu', with point after the `u'.
> > M-TAB ; you see all completions for all faces, not the 
> > faces that start with `cu' or that have substring `cu'.
> 
> No, I see completions starting with "cu".
> We must be doing something different, but I don't know what.  I typed:
> % emacs -Q
> M-x customize-face RET font-lock-comment-delimiter-face RET
> click on "font-lock-comment-face"
> C-a C-k
> c M-TAB u M-TAB

I'm using the latest Windows binary:

In GNU Emacs 24.0.93.1 (i386-mingw-nt5.1.2600)
 of 2012-01-29 on MARVIN
Windowing system distributor `Microsoft Corp.', version 5.1.2600
Configured using:
 `configure --with-gcc (4.6) --no-opt --cflags
 -ID:/devel/emacs/libs/libXpm-3.5.8/include
 -ID:/devel/emacs/libs/libXpm-3.5.8/src
 -ID:/devel/emacs/libs/libpng-dev_1.4.3-1/include
 -ID:/devel/emacs/libs/zlib-dev_1.2.5-2/include
 -ID:/devel/emacs/libs/giflib-4.1.4-1/include
 -ID:/devel/emacs/libs/jpeg-6b-4/include
 -ID:/devel/emacs/libs/tiff-3.8.2-1/include
 -ID:/devel/emacs/libs/gnutls-3.0.9/include --ldflags
 -LD:/devel/emacs/libs/gnutls-3.0.9/lib'

Are you?

Actually, even after typing `c' and hitting M-TAB (your recipe and mine), I see
all possible font names, not just those containing `c'.

And after typing `u' and hitting M-TAB again (still with point at the end, i.e.,
after `u'), I still see all possible font names, not just those with `c' or `u'
or `cu'.

Again, I must move point to be _before_ the text for M-TAB to match it (as a
substring).  Before `c' with only `c' present it shows all font names containing
`c'.  After `c' with only `c' present it shows _all_ font names.

Before `c' with `cu' present it shows all font names having substring `cu'.
Before `u' with `cu' present, however, it shows _all_ font names (not just names
containing `u'), and it moves point after the `u'.  After `u' with `cu' present
it shows _all_ font names (same).

See attachment.

Perhaps the problem is platform-specific?