It is true that Nagato used Madara's eyes.
However, there is no plot hole regarding Jiraiya.
You say that Jiraiya should have questioned why Nagato had the rinnegan, but let me ask you this:
How was Jiraiya supposed to know the requirements to awaken a rinnegan? How should he have known that an Uzumaki alone can't awaken the rinnegan? Did he even know that Nagato was an Uzumaki to begin with?
The only people who we know to have awakened the rinnegan are Momoshiki, Hagoromo, Madara and Sasuke.
There is no way that Jiraiya would have even known of Momoshiki's existence (or the existence of the Otsutsuki clan in general).
In order for Jiraiya to know how Hagoromo awakened the rinnegan, he would have had to have known about Kaguya and the Shinju, and I highly doubt that Jiraiya knew about that stuff.
Madara was thought to have died to Hashirama and almost nobody ever knew at the time that Madara had ever awakened the rinnegan.
Sasuke wasn't even born at the time, and by the time that Sasuke awakened the rinnegan, Jiraiya was already dead.
Now having said all this, I reiterate my questions:
How the heck would Jiraiya have known the process for awakening the rinnegan, and how would he have known to question Nagato's possession of it?
