We have never heard it mentioned that there would exist a substance, object or other that could
not be replicated. Things like latinum, dilithium or other supposed valuables are no exception there.
We probably have to assume that there is a different cost on the replication of different items, in terms of processing power, sheer energy, and possible raw materials used per item or kilogram. Thus, replicating of latinum is a non-starter because replicated latinum would cost more than it is worth. That's more or less the logic behind nobody today mass-producing counterfeit money, too: all safeguards can be bypassed (the authentic bills were printed by
somebody in the first place!), but it's just plain not worth all the effort.
It would then follow that living persons could be replicated, too - it would simply be awfully expensive. An industrial replicator (one of those rare things that the Maquis deemed worth stealing from Starfleet in "For the Cause") might have to spend months doing it, say. We do know that living tissue can be replicated for medical purposes. TNG "Ethics" and VOY "Emanations" show this being done, the latter as a matter of routine by a damaged starship stranded far away from the usual resources. On the other hand, there are practical limits, and the same technology that in VOY "Emanations" produced working spinal matter for a random alien failed in VOY "Phage" to produce a working lung for Neelix. Perhaps some other UFP replicator in a well-equipped hospital could have done that lung - but it might still have been cheaper and faster to produce it using some other technology, such as cloning.
As for the difference between replicating and transporting, the latter seems to require an original that is the same as the product. The former creates the product either out of pure energy or then out of an original that is different from the product (say, a barrelful of hydrocarbons might become a sandwich). We have some evidence that things are created out of pure energy on occasion. In TNG "Night Terrors", the E-D is said to normally possess the ability to reproduce elements; if this happened by taking one element and turning it into another in a replicator, the proper term would be "transmuting", not "reproducing".
Then again, we have seen an ordinary food replicator turned into a transporter, in DS9 "Visionary". The two devices might really be one and the same, and the replicator just modifies the signal much more extensively than the transporter does: hydrocarbons to sandwiches, rather than infected lieutenants into healthy ones or armed Klingons into disarmed ones.
Isn't it possible to tell if something is replicated or not?
We don't know. Some people claim they can taste the difference, but they may well be lying to themselves, and would fail a blind test.
Certainly it's difficult to tell a difference for real in, say, TNG "Data's Day" where a lot of forensics effort is needed before our heroes can declare that the blood they found was faked. But by the same token, it's difficult to fake things so that they would pass muster in all cases - even when it's the all-powerful Romulan Tal Shiar doing the forging.
The mirror case comes from DS9 "In the Pale Moonlight" where Sisko tried to forge a datastick, using the best experts he could find, and a single Romulan with his portable resources was able to declare it a fake. Then again, that Romulan may have been lying - he didn't need to prove the thing was a fake in order to declare it a fake.
Usually, it doesn't matter. In DS9 "Rivals", Quark tells the food replicator to replicate an alien device, and the food replicator obliges, even creating enlarged versions thereof. The results are fully functional, even though neither Quark nor anybody else in the Federation (least of all the people who built that replicator) knew how the alien things worked! So most of the time, standard resolution is sufficient...
Timo Saloniemi
