The only answer to the riddle that makes any sense to me is a young duck, or duckling. Behold my "theory", and be sure to read till the end of it all if you are on the side of those that want to argue that in the movie Lessing himself said that a duck wasn't the correct answer (and neither was the platypus).
Also keep in mind that Benigni has explained the riddle only as a "nonsense" that appears at a point when Guido expects a more rational response from Lessing. He never actually gave the answer. So for all we know, there maybe isn’t even one! (Carlo Celli http://www.findarticles.com/p/articles/mi_m0412/is_2_28/ai_ 64688898/print )! Nevertheless, here are my humble thoughts on the matter, as formed by the previous threads and fine-tuned by quite some searches throughout the internet:
For a good start, I think we should (as Rlkurtz says) base the answer on the Italian words spoken in the movie, since that is the closest we can get to the original and is therefore the most accurate. Those of you speaking more than one language will confirm that you can simply not translate proverbs and sayings too literally. For example in English they use the expression "painting the town red" to describe a wild night out in the city, while in Dutch they would use (literally translated) "putting the flowers outside". I think you know what I mean. Therefore:
Grasso, grasso, brutto, brutto, tutto giallo in verita, se mi chiedi dove sono ti rispondo qua qua qua.... Camminando faccio poppo, chi son io dimmelo un po'
Let's brake it down:
Grasso, grasso: Fat, Fat
Twice mentioned, most likely because the riddle needs some overall rhyme and structure to it, these words could apply to many things of course. Some of you have proposed a member of a nation, and true, we all have seen the fat German eating his bratwurst and drinking his huge beer; but I'm sure there must have been fat Jews in those days as well. In fact, does anybody know when McDonalds started, because I’m sure there were some obese Americans hanging round somewhere  (no disrespect intended!). In fact, you have to be honest and admit that virtually all races know fat people, yes, even us Belgians. But let's not forget, also animals can be fat. And without summarising the full list of candidates, I would like to point out that in my opinion ducks (and similar species), have this typical wiggly woggly, side to side walk, a bit even like overweight people. Donald Duck flashback anyone? Furthermore, unlike chicken or other lean meat, the meat of a duck is quite high in calories due to fat, useful for his life on the cold water in winter and even in summer. Trust me, I know this might currently still sound as mere speculation, but we only had one word so far! So let's get on with it.
brutto, brutto: ugly, ugly
Again twice mentioned, most likely for rhyme and structure as before. This time I'll make it brief, because we all know ugly people, and we all know ugly animals. But wait, isn’t there one animal that comes to mind when thinking of ugly? Haven't you ever heard that Hans Christian Anderson worldwide known fairy tale, about that UGLY little duck that turned out to be a beautiful swan? Sure, it could still be coincidence, but for now it's more appropriate than any of the other suggestions, no?
tutto giallo in verita: completely yellow in reality/truth
Some of you are saying that being all yellow has something to do with being afraid, being a coward; and if the saying was originally in English I would say you’re correct. But note that the original is in Italian, and as Tazlima says, in Italy yellow isn’t used to mean chicken, they call them rabbits! Some of you say that the yellow is referring to the clothes, or the star of David, but neither Jews nor Nazi had anything noticeably yellow on them! The star of David is usually white. Even the painted Jew horse (Robin Hood) was green if you need any colour at all! That brings me back to the duck. What is the colour of a little duck? Or chicken? Yellow. Easy to see, but we think too far. This is now the second time the “duck theory” is closer connected to a part of the riddle than any other suggestion.
se mi chiedi dove sono: if you ask me where I am ti rispondo qua qua qua: I respond to you qua qua qua
This would imply that in some way, the answer to the riddle, whatever it is, can be posed a question and an answer can be expected. I think this could rule out anything non-living, because first who’s going to ask a question to an inanimate thing, and second, what inanimate thing will respond back to you?! This only leaves humans and the rest of the animal kingdom (with audible reactions) to choose from. If I now told to a 5 year old child, that I had asked a question to an animal, and the animal responded qua qua qua, or kwaa kwaa kwaa, or however else you want to write it, what do you think the answer will be? Once again, our duck. To the people tempted to find a much more intricate meaning to qua qua qua, and bringing out translations that mean “where”, or “here” or some Italian slang that means “cheap” I can only say that we’re trying to solve a (children’s?) riddle here, don’t search too hard and too far. It’s not rocket science!
Camminando faccio poppo : while walking, I make “poopoo”
Unless we know all possible meanings of the Italian word “poppo”, there’s not much we can do here. Strangely there’s nothing to be found in any of the many online dictionaries. Help us out here Italians! The word poo reminds me a bit of the word pooh (not sure how to write it, and not referring to Winnie, but I mean faeces). Is it not possible that ducks, unlike many other animals, keep on walking when going for message number two? I must admit that this part is just guessing, just trying to make some sense here, don’t break down the whole theory on this one speculation. One reason to back this up however, this riddle was sent to doctor Lessing by his friend in Austria, a VETERINARIAN! If anybody would know or would have any detailed knowledge of an animal, besides Ace Ventura, surely your average animal doctor would. And doesn’t this in general also once more augment the chance that an animal is the solution to the riddle? Funny coincidence on the other hand, when entering “poppo” in Wikipedia, a link comes up to a Japanese site depicting a Pokémon birdlike character http://en.wikipedia.org/wiki/Pidgey Largely irrelevant this last bit of info, I know, but thought I had to share it anyway.
chi son io dimmelo un po: who am I, tell me a “po”
Although the first part is quite easily translated, in the end of the riddle the “po” word has been used once again. This has of course a negative effect on the clarity of the translation, although I personally think this time it’s used more to make it rhyme instead of adding any deeper meaning. If I would have to translate it, I would use the word “little” (from the French word “un peu”). Could even reflect on the duckling when being little.
And there you have it, my explanation as to why the answer is a duck(-ling). That now leaves us with one problem, why Dr. Lessing said in the movie this answer isn’t correct. The only argument I can offer, as to why, is the following:
Any good/close friend of the doctor, knows how obsessed he can be by riddles. He would leave his sleep, endanger his health, do anything for it. His importance for riddles is clearly shown in the movie when Guido Orifice is serving the group of Germans, and Dr. Lessing wants to tell him an “important” message. When the doctor deliberately knocks a bottle of whisky (or whatever) down, Guido runs to him, expecting some help, some way out of that hell he’s in, for his and his family. After all, he and the doctor were relatively good friends before, surely there must be something more he can do besides getting him a job as a waiter. But what important message does he tell him? That he hasn’t found the answer to a stupid riddle! In a time when millions of innocent people get killed, he thinks of a trivial rhyme! How can you mistake the expression on Guido’s face for anything else than disappointment! He couldn’t care less about that answer, he’s not thinking it’s a Nazi, or Jew, or duck or whatever. His only chance for rescue turns out to be nothing more than a senile old man, unable to do anything for him. No longer friends. And I believe some similar situation has arisen between the doctor and the veterinarian. The veterinarian in Austria simply is no longer a friend of the doctor. That veterinarian has woken up and realised what the Germans are doing, and can no longer maintain his state of friendship while he almost certainly knows (as friends tell each other secret things) what the doctor is doing more or less. Or even if the doctor did not tell him, he found out himself. So he decides to give him some kind of punishment and uses one last very simple riddle, gives it to the doctor, who guesses it correct at the first attempt, only to reply that it’s not the correct answer! The doctor of course , having this long history of riddles between the two, automatically believes him, and continues to look further for the answer till it drives him crazy. The veterinarian knows this would happen, and with it effects a successful personal punishment. I do realise the answer to this riddle is not as witty as the "silence" riddle; but maybe that’s all part of the plan!
I most eagerly await any comments and further suggestions anyone might have. I have indeed not slept myself for one night to write down all of this, but it will be my one and only, unlike the doctor 
Best regards
Didier
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