For example, if I copy a 168mm wide item from ID and paste into PS CS3, the PS document created is 1984px wide at 300dpi.
The same item pasted into PS CC creates a document 476px wide at 72dpi.
No a docuent has one and only one DPI setting. If the document you paste into has a 300DPI resolution and you past into it from a 72 DPI document Photoshop will match the document DPI. The document DPI does not change its still 300dpi.
168mm = 6.61417" at 72dpi that would be 476.22024px your 476 pixels. It looks like the way your pasting Photoshop is not scaling the paste up to match the document resolution and is just retainning its 476 pixel size. 476Px at 300DPI is 1.59" about 1/4 the original 6.6" size. To retain the original 6.6" size the 476PX need to become 1980PX. So if Photoshop failed to scale the new layer you can use free transform on the new layer set the width and height to 1980/476 = 416%. 300DPI/72DPI=416.6%
Free transform poses problems when pasting into multiple documents though. For example, when creating graphic email footers, they all need to be exactly the same size. If I paste from ID into a correctly sized PS doc and they appear smaller, I then have to manually enlarge them all by eye which will result in them all being slightly different sizes.
The fundamental problem is the difference in the way CS3 and CC act when copying and pasting. I don't know of it's a problem with copying from ID or pasting in PS, but the CC method just isn't as usable as the old version.