I haven't seen the anime, but IIRC, in the game he doesn't figure out that Ikusaba Mukuro and Enoshima Junko are actually twins - Enoshima is the one who explains that.
What he does notice is that:
1) In the photos, the only person whose face is never visible, in any of them, is Enoshima Junko.
2) The were 9 bodies in the morgue, but 10 people had been killed. One of the bodies had disappeared - where?
3) After examining Ikusaba Mukuro's corpse, Kirigiri said that the knife wound seemed to have been inflicted after she had died. The only other possible cause of death was the multiple smaller wounds that had been inflicted a number of days ago.
4) Given that there was one less body than there were deaths, and that Ikusaba Mukuro had apparently been killed several days ago, by multiple smaller wounds - much like those you would suffer from being impaled by multiple spears - and that this pattern exactly matches only one of the people within the building, Naegi logically concluded that the corpse belonged to that person. The person who they had thought was Enoshima Junko. This was corroborated by the fake nails the corpse was wearing - identical to those Enoshima had had at the time she was killed.
5) However, given the corpse had been confirmed to be Ikusaba Mukuro, thanks to the tattoo on her hand, that meant the real Enoshima Junko was the only person whose whereabouts were unaccounted for - and therefore, the only possible culprit.
It's not like Enoshima Junko and Ikusaba Mukuro were identical twins. They were twins, and they presumably looked similar, but not identical - they just had no real memories of seeing the real Enoshima Junko, and she was not visible in any of the photos, so they had no way to know that the Enoshima Junko they had met was an imposter.
And the reason they didn't immediately recognise the Ikusaba Mukuro in the pictures as being the Enoshima Junko they had met was presumably because of the totally different hairstyles etc, and copious amounts of makeup. It's certainly easy to believe they wouldn't notice unless it was pointed out, when you consider the huge difference between the two characters.
As for why they traded places, I can't actually remember exactly, but I believe it was because Enoshima was planning to kill Ikusaba from the beginning and use her death firstly as an example to the other students of what could happen to them (to terrify them into doing what they were told), and secondly to disguise Monokuma's real identity. If everyone had seen Enoshima die right in front of their eyes, there was no way they'd suspect she was actually the one controlling Monokuma, after all. So she used her authority as the superior, and as the elder twin, to make Ikusaba take her place, and then killed her when she wasn't expecting it.
And we use spoiler tags partly because it's just common courtesy (someone might accidentally stumble across this who hasn't seen the latest episode and be spoiled - it's happened to me in the past), partly because what we're discussing hasn't been entirely explained in the anime yet anyway AFAIK, bearing in mind I haven't watched the anime, (so if you haven't finished the game, you'll be spoiled), and partly because it very clearly says in the forum rules that you must use spoilers for this kind of discussion.
