If you are trying to register an image that has no distortion in it, then you only need a 1st order transformation normally (an affine transformation). As you more to higher orders in an attempt to reduce rms error, you will effectively start to introduce distortion in the areas away from the control points. Most people erroneously think that the higher the order the better... wrong. The examples in the help file will give you some visuals and a good explanation. If you examine your control point information and the rms data, you will find that you may have one or two control points are causing the 'issues' but it is better to stick with a 1st order if it works well and if a 2nd order introduces distortion (particularly along the edges) you will know you have gone too far. If you want to see some real fun stuff, ramp up the order and watch the warping increase.
So my recommendation, if the images don't contain distortions, then stick with registering and start with an affine (1st order) and only move up the order if you have ruled out erroneous control points and 2nd improves things.
Fundamentals of georeferencing a raster dataset—Help | ArcGIS for Desktop
The next thing to read is
Fundamentals of orthorectifying a raster dataset—Help | ArcGIS for Desktop
when you know that simple rectification isn't going to cut it.