I'm having a problem with LR 4 (currently at 4.1) which I've not seen with prior versions. Background:
Windows 7 64-bit
NVidia GeForce GTX 560
Two Dell 2408WFP displays
Color managed using Eye-One Display 2
I've been noticing harsh, overly saturated and contrasty colors in Lightroom. I wondered if the new process version was responsible, but then I realized the image quality on my secondary display was very good.
I decided to try swapping monitors. After again recalibrating the exact same issue continued. It seemed to be only Lightroom showing this problem. I then hit upon an oddity that convinces me the issue is LR.
I un-maximized Lightroom, making it just a small window. I then dragged that from my left, primary monitor to my right, secondary monitor. While holding the mouse button down to drag, the colors still look bad, but as soon as I release the button, LR re-renders the image and the colors look fine. I can do the same going from the right monitor to the left. When I release the mouse button, the colors turn bad.
Further pointing to LR, I was able to Shift-Prtsc to snap a pictured of the desktop which I did with LR in both positions. I used Photoshop to crop to part of the LR window and I'll attach those images. Left is primary, Right is secondary.
It appears LR knows which display it's on, and it's rendering differently accordingly.
What happens when you drag some other colour-managed app from one window to the other? Make sure it's colour-managed. PS would be a good candidate. It could be that the profile for your left monitor isn't being set properly, in which case LR would indeed change the look of your images as you move from monitor to monitor.
Others are fine. That why I also emphasized that until I let go of the mouse button, the color matches what it was on the other monitor. That wouldn't happen if the monitors weren't calibrated right. At that point, the window re-renders. If it was only a color shift, I'd be less concerned, but this is a change in the saturation and contrast as well.
I still have LR3.6 installed and I just loaded it and imported this photo (since I know it exhibits the problem). In ver 3, it works as expected.