Get Rid of Fringe Pixels
In many cases you can remove that fringe by going to Layers> Matting> Defringe. Try using the default setting of 1. That will often do the trick, but if not, choose Undo (from the edit menu) and go back and try a Defringe setting of 2.
If Defringe doesn’t work, or the edges end up looking a little jagged, here’s another alternative to Defringe.
Command-Click on the Layer name in the layers palette to load a selection of the contents of the layer. Then from the select menu, choose Modify>contract and contract by 1-3 pixels. Go back to the select menu and choose inverse. Press Command-H to hide your selection then add a very slight Gaussian Blur (Filter>Blur>Gaussian Blur) of 1 pixel or less.
Here’s another variation on the same theme. Command-click on the layer name in the Layers palette to load a selection of the contents of the layer.
Then from the select menu, choose Modify>Border and enter 2 for the value. In the layers palette switch to the Background layer, then press Command-J to copy the selected area on to its own layer. Move the "border layer" above the fringed layer and change mode to Lighten to hide a light colored fringe, darken to hide a dark fringe.
Remember More Files
By default, Photoshop remembers the last 10 files you’ve opened. Actually, that’s not quite true: it remembers 30 files but only shows you the last 10 because that’s the default preference. To see a list of the last 30 files you gave worked on, press Command-K to open Preferences, then press the Next button to go to the file handling dialogue. At the bottom you’ll see that the "Recent file list contains" box is set to 10. Change that to a 30 and you’ll have a nice long list under File>Open recent.
Paint Away Color
When you’re working on a color image, you can use the brush tool to selectively "paint away" color so that the image looks black and white. With the brush tool active go to the Options bar and change the Blending mode from Normal to Color, use Black as your Foreground color, and start "painting away" the color.