Something I've played with that possibly has relevance:
I set my PS Color Space to Prophoto RGB for something I was doing.
Then, I did a screen capture for some reason and then pasted the image into a New Photoshop document, and the image has the horrible reddish cast. And then, when I save the image and upload it a browser, it looks fine in IE but not in Firefox, meaning that something is wrong with the Color Space.
So, I played around a bit. I tried converting the profile of the document/image to sRGB -- Photoshop "sees" that it's ProPhoto RGB. Anyway doing a Convert to Profile didn't "work", but do you know what did? Doing an Assign Profile worked!
So, what happended: I had set my PS Color Space to Prophoto RGB and so the new document I created to paste the screenshot into was in the ProPhoto color space. Then, when I pasted the screenshot in, the actual image was in a different color space (I assume that of my monitor) and the two didn't "play well together"!!
But as soon as I did the "Assign" function the image looked just fine (and would in a color-managed browser)!
Now, the "new document", which is the Background layer, was not converted to sRGB. In other words, if I was to try to create some kind of composite, one with a ProPhoto image and with another image with a different profile, then i'd have to do some "housecleaning" by making sure everything was using the same color space and, for the Web, converting it all to sRGB. But, in this case, more work was required than just converting -- I could have cranked down on the Reds, but Assigning a profile worked quickly.
As an aside, the reason why assigning the sRGB space worked well is because I'm working with a relatively cheap new monitor (replacing my old "good" monitor) and for now I haven't calibrated it, I just adjusted the Brightness down to a decent level -- my colors look reasonable. So, it's using a default system display profile, which obviously is derived from sRGB, rather than a "custom" profile.