Presumably it wasn't quite there yet. After all, it seems that Orochimaru was intent on unlocking a power beyond either clan's, yet Shin clearly showed that such power could not be awakened that way. Which is why he wanted Itachi, because he had such powerful eyes. It seems that Orochimaru thought that he would need a live uchiha and not just some intermediary.

It also seems that while Shin would make a good vessel, initially he wanted to use Kimimaro but that fell through, and Sasuke was next but it took too long. Once he was ready for Sasuke, Sasuke killed him. In short, there was no real opportunity where he could've use Shin. While he may have been able to use a Shin in stead of an unnamed shinobi, it seems that Orochimaru was unwilling to risk a precious body.

Furthermore, it's not clear what the timeline of Shin is, it's possible that the cloning came only after he was revived.

Not really, we have a clear evidence that Shin's cloning was happening quite a while before this, since Oro stated that he transplanted Shin's arm to Danzo along with the Sharingans and Hashi's cells within it, meaning it transpired during the times when Oro was still a Konoha shinobi.

There is no reference to when the cloning started. We know that arm contains Sharingan and Hashi cells, so cloning wasn't the only experiment on Shin. It's entirely possible that the cloning only happened after Orochimaru's rebirth. Or it could've happened after Orochimaru captured Sasuke, as Orochimaru was hellbent on making Sasuke his vessel and so would not have taken a shin.

Either case would explain in a very reasonable way why he didn't take a Shin.

EDIT: the clones don't look very old, around 12-15 to me, so that would put their birth around the 4th war, give or take a few years. They don't seem to have been aged artificially, as no mention of that is made. So they also would not have been available as vessels around Sasuke's candidacy, and it seems orochimaru was not yet done with his experiments on adult Shin (as evidenced by kabuto's advanced cocktail of powers and the fact that Orochimaru obviously would've wanted such for himself). So, he wouldn't have taken Adult Shin and wouldn't have been able to take baby shin clones as a vessel.

But why didn't Naruto think "Oh no, Orochimaru is getting back to his old tricks, I should do something about that".?

He wasn't getting back to his old tricks. He even calls it an old experiment. It's likely that this whole cloning happened before his pardon, and so is covered in it. Orochimaru did nothing wrong. Also, Shin consented to his experiments, so there's nothing wrong with that either.

It's as Orochimaru said in Sasuke Shinden - the leading powers let people like Orochimaru free because they are mavericks and the only ones able to deal with unorthodox problems should any arise in the future. Therefore, I don't think they'll mind him bending some of the established rules, but people like Naruto will never allow for him to cross the line in any way.

If he cloned Shin before his pardon (and the age of the Seems to confirm that), then he didn't break any rules, assuming there's a rule against cloning.

while the leaf is constantly watching Orochimaru, he is still none the less the leader of his own hidden village. and still conquered an entire nation. so presumably if they just causually tried to arrest him,they would most likely be dealing with an international incident. on top of that cloning isn't stated to be illegal and as long as no one is getting murdered, why would they care if he was cloning or doing such experiements. not to mention such experiments could have vast potential in the medical industry. just imagine if the cloning processes is so advanced they can clone individual body parts or organs. people who need a transplant could potentially get a brand new organ or body part.

i was under the assumption the adult Shin was a regular human that was a follower of Oro and that Oro only cloned him, not that he was artificially made.

Yea Shin is a normal human (as far as that applies), and got experimented on heavily. He was then cloned. So the other shin are artificial humans.

Mitsuki seems to be a product of the Shin experimentation.