The worst thing I see is when someone cuts an element out of an image and it looks like it was literally cut out. The best example is an image of, say, Mom that you want to cut out and put on a beach image of Tahiti. :P
You can avoid that cutout effect and have Mom land well on any background image you choose, within reason, by following this easy technique:
- Make a selection of Mom from an existing image (I recommend using Quickmask, pretty easy, just takes patience)
- choose Layer>New>Layer via copy
- hide the original layer. Now you'll just see Mom and no other elements from the original image.
- select the layer (CTRL-Click the layer) and all pixels on that layer are selected
- choose SELECT>MODIFY>CONTRACT and choose 1 pixel
- choose SELECT>FEATHER and choose 1 pixel
- choose SELECT>Invert Selection
- CTRL-X (cut)
This blurs the outermost pixels of your cutout to blend in more nicely to whatever background you choose.

You may not be able to notice the effect until you drag and drop this layer into another open Photoshop image. Try it out!
Have fun!
Sahavay