Dr. Nick: The ratings are falling! Insert some accidental groping!
Xard: Whatever the in-universe reasons for the act were (I think simple curiosity is enough) I think there's important thematic subtext in this scene/act and with Gendo's old glasses in general and what their usage says about relationship between Shinji and Rei in this two-ep "Rei Arc". For one there's Shinji's symbolic "identification" with Gendo by the act of putting glasses on - given what follows right after the Oedipal overtones are hard to miss.
More importantly however Gendo's glasses work as a medium that conveys what defines relationship between Rei and Shinji at this point. Or to be more specific, how they see each other. The previous scene in the episode where Shinji literally observed/gazed at Rei was defined by Gendo's presence and bewilderment and jealousy Shinji felt when he saw Rei talking with Gendo. "Who is this girl and what is her relationship with my father?". This is the main driving motivation behind Shinji's wish to know more about Rei.
In other words: Shinji sees Rei first and foremost through "Gendo" and nature of his connection with Rei,
and in this scene Shinji sees Rei through Gendo's glasses which symbolize him throughout the series! The fact Shinji put on his glasses also is literally the trigger for the first real interaction (haw haw) between the two.
( And of course the fact they needed something that would get us the uncomfortableness of what soon happens is important factor )
Kendrix: Thanks for pointing it out, but I'd interpret this a bit differently: When you put on someone else's glasses, you see the world as blurred as their owner sees it without glasses.
This glasses are Rei's most valuable possesion (they were placed in the way of the only ray of light entering the appartment. Someone's house is aways a private place that shows that person's way of living, an intimate 'inner sanctum'. And the glasses are the relic of Rei's sanctum) and perhaps Shinji even figured out that they're Gendo's.
He's trying to understand both Rei and Gendo, so him putting the glasses on could simply mean that he's trying to see the world through their Eyes, which is what the eloborate perspective cut is meant to emphasize - and of course, while he has been fascinated by her all the time, her connections to Gendo are a further incentive for Shinji to seek her out - He wants to become part of Gendo's world, his efforts to 'see the world like Gendo does' are one of the many things that draw him to Rei, a person that Gendo puts his trust in - However, I don't think Rei's connections to Gendo are EVERYTHING that intrests Shinji about her or influences the way he sees her. He is about to make his own experiences with Rei.
Xard: The other half of this interprepation depends on ep 6 and so I can't really touch it yet. In fact it was the ep 6 scene that initially gave me the idea. In any case I don't think the full picture I got is compatible with this, though I'm not 100% sure.