I believe many episodes alluded to the fact that the transporter not only transports matter but "energy" as well.

Patterns degrading in the buffer.

Scotty's pattern in a loop rescued from a crash on a dyson sphere.

Kirk's split "Mirror Mirror" That one violated the law of conservation of matter but it's fiction.

One of the wierd ones was Rikers transporter bounce split where he was recovered and there were two Rikers both who considered themselves to be the real Riker one of which eventually went to help the Maquis.
That one violated the law of conservation of matter but it's fiction.

Voyager used the transporter to hide telepathic aliens from persecution.

Dr Pulaski was saved by using the transporter from the aging type of reaction from the advanced immune system attact from hybrid humans.

I always thought the transporter was underused as a medical tool.
They always had some sort of excuse why they couldn't use it like radiation, or in Worfs case they wanted the alien to heal him.

Latinum couldn't be replicated I can't remember why but it figures.