Rotate a picture by a small number of degrees

You can rotate by degrees in Paint by using the Skew command. Click Resize, and place a value in the horizontal and vertical fields.

To maintain the look of your image, use equal values, one negative and one positive.

For example:

Horizontal=10, Vertical=-10.

In GIMP, select the whole picture or crop of the picture. Select the "Perspective Tool" (menu Tools -> Transform Tools -> Perspective), and adjust the skew , and rotations (see rotations next) by adjusting each of the 4 corners as needed. In GIMP 2 you can do this live and see the results, then hit transform to finish.

For small rotations, and better control of just the rotate, before or after adjusting the skew, use the "Rotate Tool" (menu Tools -> Transform Tools -> Rotate), which can again be rotated live, then transformed and has entry box for small rotation adjustments.

Irfan View is free and can rotate by up to 0.01 degrees.

However, since you mentioned stretching one end of the rectangle, it sounds like you're beginning to see the issues of camera lens distortion. Have a look at this page on barrel distortion - the examples really are worth 1,000 words (disclaimer: I'm the author of the page).