With GET requests, you frequently run into URL size issues. IE has a roughly 1800 character limit, which is pretty easy to hit with machine-generated data. I remember going through hell with JSF charting frameworks, trying to squeeze the serialized data down under 1800 characters. Eventually we gave up, pulled everything out of the serialized data (it still took up over 1K though, just through framework metadata, and so only left us around 500-800 bytes to play with), and threw it into query parameters that we could control ourselves.
This isn't an issue with POST, but then you run into the normal POST issues with refreshability, bookmarkability, and portable URLs.
A possible elegant solution is suggested in the paper: store the continuation on the client. I don't know what problems this presents in practice.