Veneer repair  

I used..
I used a clever french polisher called Phil. I think he ironed it on or something. He went on and on about it, so I missed a lot of what he said when I drifted off occasionally.

Thanks for the replies, guys...
Obviously, if I transplanted from a more inconspicuous area I would repair it with a new veneer. Am I being too OCD here?

Knock yourself out.
I wish you good luck.

I have also had success....
at patching veneer. I taught myself, read a lot and after a bit of trial and error I have had results good enough to sell on - and none of my customers has been able to see the patch until it was pointed out (i'm not blowing my own trumpet here, just suggesting it's doable and not that hard to get decent results).
Depending on how much time you want to spend and the extent to which you want an invisible repair then I would suggest a different approach on the top surface and the smaller dings on the vertical surfaces (just because they're smaller).
For the smaller sections you could minimise the effect of the damage by using some darker wax polish to colour the underlying carcass wood. The ding would still be visible but would just be part of the history of the piece. Alternatively, you could fill these smaller dings with Wood Stopping (not sure what you'd call it on that side of the pond) and then try using stain and coloured permanent markers - the difficulty here is that you have lighter grain flecks in the wood which would be very difficult to do.
With the larger patch the veneer has torn along the grain for a distance and then goes in a jagged diagonal line to the back edge. The restoration book I read suggested cutting the veneer in a diagonal path across the grain, not directly across the grain, and I have followed this advice successfully. On your repair you could just take off the few jagged bits - using a scalpel and a metal ruler - and end up with a right-angled trapezoid shape (google "right angled trapezoid" to see what I mean). Getting the grain of the patch to match the surround would be tricky but you could use permanent markers to carry grain lines across the join (instead of permanent markers try to find some woodworking stain or dye pens which can be used to disguise small blemishes). BTW the "permanent" pen marks can be removed easily with methylated spirits (think you call it mineral spirit on your side of the pond) so you don't have to get it right first time (but try this in an inconspicuous place first just to make sure you can get it off - and that the mineral spirits doesn't take the finish off your furniture!!).
You could also ask your question in the forum at www.refinish.com - they are very helpful but I found them a bit "strip it down to bare wood and start again" gung-ho so be careful.
If you are just too worried about making the damage worse then take it to your local antiques restoration company.
Small Print....BTW none of the above constitutes advice. You should seek the advice of a professional restorer before carrying out any work.
Cheers,
Paul.

Well, I talked to a veneer expert today...
He came very highly recommended from a friend of mine. The quote for the entire top(in trying to match the rest of the piece) is $600. And funnily enough, only $900 to reveneer the entire piece. Doesn't seem too bad to me. It'd be almost like having a brand new piece. I'm just not sure I want to go ahead with it. What do you lot think?

I assume
the total re-veneer is done over the present veneer. The new veneer will be quite thin, and the piece will still be thicker than it is now. Is this acceptable ?
I'd save the $300 and let them repair it. That way you'll have the original look of the piece, and some honest minimal repairs, rather than completely hiding that nice original material -- and changing the substance of the piece in the process;
Just my opinion. . .

Actually, SDR...
The quote includes stripping of the old veneer. I'm seriously considering the whole piece.

That's a 4753 or 4754 desk, right?
I don't know much about them... Are they hard to find? Expensive?