The overall aesthetic seems consistent and gives the nostalgic feeling of the show. The design choices of image and text support each other well.
I think the most effective sheet for legibility is Joey's quote. You did a nice job of placing the white text on a solid dark red background (placement technique), which makes the text easy to read. Ross and Phoebe's quotes are over busier sections of the images, which make them a bit more difficult to read. I would consider changing the placement of the text or the treatment of the background. Maybe with Phoebe's you could have a gradient with the darker part at the bottom so we can see her face and then the text will also be emphasized?
Also, in Phoebe's mobile image, I think you have a default "text" box that shows up in Photoshop. Easy fix!
With Phoebe's web image, is the TNT HD logo intentional? I would either have it for all of them as a reference or none of them to unify the aesthetic.
I think the treatment of the typeface is good. I might consider giving the name of the speaker a little room to breathe below the quote. It seems like it is infringing on the space of the quote.
I consider the picture to be background and the text to be foreground, which makes sense. Since the images are from television sets, they are a little busy. I would take another look and make sure that the text is not competing with the image that it is over, especially in Ross and Pheobe's quotes.
This seems like it should be pretty manageable to build. I think that some of the images look a little fuzzy. I'm not sure if this is a function of the quality of the image or of the treatment of the image, but I would look into seeing if you can make them a little sharper.
I would take another look at Ross's mobile image and see if you can work with the left edge. It looks like it is about to cut off his eye, and I worry about how this may transfer to certain mobile devices. I would see if you can give it a bit more room