I hope this is the right place to share this.
I have 3 WordPress driven sites that I have upgraded to WordPress 2.5 this week, and I had the same problem that others had, that when I clicked the insert into post button on the media manager, the popup window went white, and stayed there and nothing else happened.
Having tried all the solutions, and having found it worked now and again seemingly randomly, tonight I discovered a scenario I could reproduce and a fix.
Typically I have Firefox open on my main website, and then I open one of the other sites in another tab. When the site I am editing is on the second tab (haven't tested further than that) "Insert Image into Post" produces a white popup screen, if I close the first tab I can then insert images perfectly.
Why this would solve it, I don't know, and this may just be a quirk of my system, but I wanted to share in case its not just me!