What weaknesses and strengths does Malcolm exhibit through his attempts to spur on Macduff, after the two learn of the latter's loss?The killing...

After Ross tells Macduff (with Malcolm present) in Act 4.3
of Shakespeare's Macbeth that his family has been "surprised" and
 "Savagely slaughtered," and that to give him the details of the murders of his "deer"
(a pun on dear, of course) ones would be to cause Macduff's death, too, Malcolm's first
response is to tell Macduff not to hide his sorrow, but to express
it:

What,
man, ne'er pull your hat upon your brows [hide your
grief],

Give sorrow words.  The grief that does not
speak

Whispers the o'er-fraught heart and bids it
break.

I assume you would
consider this a strength shown by Malcom.  He empathizes with Macduff (puts himself in
Macduff's place, knows what he's going through, and offers sound
advice).

Macduff, shocked, however, basically ignores
Malcolm and continues to ask Ross if all his family were killed--he
can't believe what Ross is saying and can't get past the news
itself.

Malcolm's next response is to offer a solution to
Macduff:

Be
comforted.

Let's make us med'cines of our great
revenge,

To cure this deadly
grief.

This may also be seen
as a strength--he is offering a solution and giving Macduff a concrete option for
overcoming his grief--but might also be seen as self-serving--he is pushing his own
agenda (lead an army against Macbeth).

When Macduff
continues to obsess over the murders themselves, Malcolm certainly makes a mistake in
interpreting Macduff's reaction, and expects Macduff to handle his grief in the
stereotypical male
manner:

Dispute it like a
man.

And Macduff sets Malcolm
straight:

I
shall do so.

But I must also feel it as a
man.

I cannot but remember such things
were

That were most precious to
me. 

He will take his grief
out on Macbeth, but first he must feel his losses. 

Malcolm
doesn't give up, however, again urging Macduff:

readability="8">

Be this the whetstone [that which your sword is
sharpened on] of your sword.  Let grief

Convert to anger;
blunt not the heart, enrage
it.

And again Macduff, the
ideal foil to Macbeth, corrects Malcolm:

readability="15">

Oh, I could play the woman with mine eyes
[weep]

And braggart with my tongue.  But, gentle
heavens,

Cut short all intermission!  Front to front [face
to face, a vital element of honor]

Bring thou this fiend of
Scotland [Macbeth] and
myself!

Macduff reveals a
sophisticated, mature reaction to grief.  He will revenge his family's murder, but first
he must feel his loss.  Malcolm demonstrates empathy, but also seems intent on pushing
his agenda.

Of course, Macduff's reaction contributes to
the theme of role reversal in the play:  his need to feel his grief before he acts on it
is typically a reaction expected of females, rather than of macho
males.