A question on photoshop

Here is a question for Photoshop experts. When I cut a part of an image using the pen tool or any other tool and when I drag it to another image to create a special effect, the new layer does not easily blend in with the background. Often The edges are too sharp before I flatten the image. How do I make the edges blend in with the background?

Instead of dragging the part you have cut, select it and click on Copy merged in the edit menu.
Then come back to the part with which you want to merge the newly cut part. Go to edit and paste. Do the necessary adjustment to align. When you are satisfied , Flatten the image. Now you will get all in one single image.
Now you can apply any special effect you want.