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Why don't you show revision diffs the way the built-in WordPress admin revision comparison works? That way looks really cool!

This has been done in v0.7! You have to add appropriate CSS to make it look nice. See the description tab for sample CSS that is similar to how WordPress does it.

Why are there extra spaces in the diff text? I have a URL "http://blah/blah/blah/", but it shows up as "http://blah/blah/[SPACE]blah/".

There is code to break up long strings so that the text will wrap better in the diff/comparison table columns. At this time, this behavior can only be changed by modifying the code to remove calls to the prd_break_up_lines function. You can read more about this at the movingtofreedom.org plugin page.

How can I show revision info for "pages?" (i.e. page.php)

In v0.8, there are admin checkbox options for placing revision info on single posts and/or on pages. (In manual mode, this is still done by placing the function calls in your page.php file.)