There are a few things that could be causing this, the most common being frame damage. Is the frame bent at all, any scuff marks near the area not sitting flush? The old screen could have similar damage allowing it to sit flush whereas a new screen would not have this damage, possibly causing it to not seat properly.
Another issue could be the quality of the replacement part. I've had parts where the frame would be lifting slightly, almost invisible to the naked eye and only noticeable after seating the screen. The side of the display frame can flex and catch on the side of the phone's metal frame. Another possibility is that the flex assembly for the front camera and proximity is loose and catching on something as well.
Last possibility I can think of without having it in front of me would be a part that was possibly manufactured outside of the proper specs. It happens a lot on copy grade parts, where the glass isn't cut exactly right or something similar.
So, in closing, check everything to make sure all components are on tight, nothing is falling apart during closing the screen, and lastly try another display assembly.