I spent a little while with the Roku app and it's definitely a bit simple: no way to advance to future dates in guide,
If you click the channel icon in the guide, it opens up a sort of "mini guide" for that and the subset of related channels. For example, all of the ESPN channels, and you can see future programs that way. Although I am not sure how far out it goes, it may only be a few hours.
Its a simple UI, but I have grown to appreciate the simplicity of it. Pretty easy to navigate and quick to respond to commands.