When Collodi wrote The Adventures of Pinocchio, his intentions must have been to point out the link between truth and reality. It is in this sense that Pinocchio wants to be a real boy (as Disney aptly reminds us more often than it should have), but it is his numerous acts of deceit that prevent him (it?) from becoming one. This relation between truth and reality remains pertinent in much of 20th century philosophy - among most prominent interests today are the works of Iris Murdoch (e.g. The Sovereignty of Good). Without going into detail that bores even those who are interested in Murdoch, it suffices to say that her depiction of morality follows the same structure as do Pinocchio's adventures: only that which is true can be real.
So today's paradox is quite a simple one. In fact, it comes from an 11-year old girl (Veronique Eldridge-Smith) who posited not so long ago that if Pinocchio states, "My nose will grow now", we would end up in a paradox. The paradox is naturally to the effect of Pinocchio's truth- or lie-telling. If the statement is false (i.e. his nose doesn't grow), then he must be lying (i.e. his nose should grow) - which amounts to him telling the truth and making us wonder why his nose grew if Pinocchio was telling the truth. Interestingly enough, her father has published a paper about this in Analysis.
Solution? None, this is a genuine paradox. There have been observations that perhaps the problem is in the statement being set in the future tense: "My nose will grow now" - and statements about the future cannot result in paradoxes as such. One can only find that certain predictions were false (i.e. Pinocchio would make a statement in form of a prediction, and not a truth/falsity statement which would amount to him being a liar). And yet, Pinocchio does state that his nose will grow now.
What we have here, one could argue, is of course not a logical dilemma per se, but rather a moral dilemma. Certainly, many logicians have been wondering about the paradox (in its broader form, known as a liar paradox); but we would do good by looking at this from a different perspective. Which brings me back to Collodi and saying the truth, looking for truth, God is truth, etc. - which are all statements referring to reality. For Collodi, and many similar statements in philosophy, there is no need to analyze the link between reality and truth. The two are interwoven so deeply that saying something true amounts to saying something about reality as well.
Pinocchio's paradox is pertinent exactly in that it breaks with this supposed truism: one can make a statement about reality which is not true - as often happens in politics. Or more forcefully, one does not need to make a truth statement in order to speak about reality (love is... cartoons come to mind). Or for Kantians among us, we can reverse that into something pertaining to morality as such: one cannot make a statement about reality that is true (but then we have to question what reality we are talking about).
So, something that can be logically paradoxical may in fact tell us more about moral dilemmas; and doing so, help us understand both truth and reality, and the relation between them.
As a side-note, Disney makes this huge mistake (which if memory serves me well is not present in Collodi's tale): Pinocchio does not become a real boy when he stops lying; he/it becomes real when he/it sacrifices himself/itself - but sacrifice is not about truth, in fact, it has nothing to do with truth.
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