Image changing after merge or flattening. How can I troubleshoot?

Question

It happened on rare occasions before but recently I had the need to reset PS to it's default settings and it's happening with greater frequency. I'll make adjustments and when I try to shrink the file by merging or flattening the color profile or luminance will change. Often not a lot, but enough to notice.
My work around was to make a stamp copy and save that, but it sometimes doesn't work.
Can anyone suggest the settings I need to check to make everything seamless? Are there any color profiles that might change in the conversion I can check? I'm most often working in RGB in 16 or 8 bit mode. It's most often adjustments to levels or curves that don't take, but sometimes filters, too.
Here's an example of my workflow with two pics. The difference is subtle but it's annoying.
Filter sky out of photo, create mask to turn sky uniform white.
Command E to merge the mask with the photo.
Create Smart Object (from photo)
Apply cutout filter. Apply notebook.
Duplicate the SO with adjustments three times.
Use Lasso to select a piece (flag) and copy to its own layer.
Set that layer on top of the stack.
Set the filter for all three layers to multiply.
The texture from the filter Notebook fails every time I merge, flatten, or send back to LR and the color comes out lighter. Here's an example from this piece.https://flic.kr/p/r6A1Zd (what I want) https://flic.kr/p/qc5QTD (not what I want).

Answer 1

Thank you for the response. I did read it right after you posted it but waited until I had yet another chance to try it out. Both times, neither solution worked.
For whatever reason PS is showing me different images when I have my layers open from when I consolidate them -- no matter how I consolidate them. It doesn't happen every time and I can't identify a pattern except that it most frequently happens if I use the filters in the gallery. Also, it seems to not be applying color adjustments.
If I zoom the image to 100% the before and after is always different. If I save it to disk in .psd or .tiff I still get a different image. When I send it to LR I have a different image from what I've been working on. It's frustrating. It can happen in RGB, LAB, or CMYK. I'm going to try reinstalling PS to see if that makes a difference, but assuming it doesn't I somehow need to make PS show me what I'm working on. Do you know what settings affect the image preview, the version I see while I'm working on screen?
FYI, I'm using a 2013 iMac, 36GB RAM allocating PS with 90% of the memory.