With respect to my colleague planetmaker, public domain is not a US-specific concept. It dates back to the first copyright law in the world, Britain's 1710 Statute of Anne, where it was referred to as publici juris ("of public right"). French jurists further developed the idea and we see the term "fall into the public domain" entering the discussion in mid-19th Century France, to refer to the fate of a creative work after all the time-limited rights reserved to the creator expire.
The problem to which I think the OP is referring is that of moral rights. Some implementations of copyright law recognise more controlled rights than the economic right - the right to exploit the commercial potential of one's creation. In particular, many jurisdictions recognise the creator's moral rights - the right to be attributed as the creator of the work, and the right to the integrity of one's work (that is, the right not to be attributed as the creator of modifications of one's work of which one does not approve).
The problem is further compounded because in some jurisdictions, primarily civil law ones, the author's moral rights are inalienable. That is, the author cannot lawfully give up those rights, however much (s)he wants to. France and Italy are examples of such jurisdictions.
In those jurisdictions, if an author says "I have no interest in this work, do as you please with it", you cannot know that (s)he intended to waive his/her moral rights. The author might know full well that those rights are inalienable, and intended only that others should have the right to profit from his/her creation. (S)he might well turn out to be very annoyed if an "unsuitable" adaptation appeared, and his/her name was associated with it without even a by-your-leave.
That said, this risk isn't huge. I don't think I've ever heard of it happening in respect of a work where the creator had abandoned his/her economic rights. Secondly, if it does, then it seems to me that changing the name of the project and removing all references to the original author will likely suffice.
But for those seeking clarity, licences like CC0 are specifically intended to implement a simple method of putting a work into the public domain in so far as is legally possible in any given jurisdiction. As Creative Commons note:
many legal systems effectively prohibit any attempt by these owners to surrender rights automatically conferred by law, particularly moral rights, even when the author wishing to do so is well informed and resolute about doing so and contributing their work to the public domain.
CC0 helps solve this problem by giving creators a way to waive all their copyright and related rights in their works to the fullest extent allowed by law
Using a licence like this makes it clear that you, the creator, are relinquishing all legally-relinquishable control of your work, and would like to go the whole way if you were permitted. Anyone who chooses to use your work can then decide for him/herself what sort of jurisdiction (s)he's in, and respect moral rights if that's what the local jurisdiction requires. Anyone using that adaptation can know that the original author intended this to be possible, and is therefore particularly unlikely to start filing suit.
Edit in response to OP's additional questions:
I have seen several people say that certain jurisdictions do not recognize the right to waive copyright and/or moral rights. But who can enforce that?
Nobody has to enforce it. In those jurisdictions, the author simply can't waive those rights, however much (s)he wants to.
Can someone other than the author sue
That will be jurisdictionally-dependent, and is beyond the scope of this site.
can the author act in bad faith claiming that the public domain dedication is legally unenforcable even though the intention is clear?
No bad faith is required. In such jurisdictions the moral rights aspect of the public-domain dedication is indeed invalid, however clearly the intention is expressed.
The utility of CC0 (and similar licences) is to clarify that the author intended to waive even the moral rights wherever possible, and is thus unlikely to sue in those jurisdictions where (s)he retains them. One could argue under the doctrine of promissory estoppel that an undertaking had been given not to enforce those rights, even though they couldn't be waived, and this might well provide a defence if a creator were ever to sue. Failing that, the mitigation measures I outline above aren't exactly painful.