Common changes caused by overexposure to magic
Polydactyly (extra digits) and missing digits
Doubled limbs, tails, heads, faces, or eyes
Bone or keratin growths all over body
Color changes in scales and skin
Diminished forelimbs or wings, which results in a deformed spine
Thickened or weakened scales
Fused scales, which causes cracking and painful skin
Weak vision/light sensitivity
Continuous growth of limbs, neck and tail (tail is most common)
Strange fat distribution (rare)
The bigger changes (extra limbs, etc) occur when the baby dragon is only a few cells, so the mutation will spread across the entire body as the cells multiply without being corrected. Other changes (messed up scales, growths, some forms of scoliosis) are caused either by mutations that occur in small groups of cells in more developed dragons or by the long-term damage done by the magic energy.
Dragons are one of the creatures in their world most affected by magic, because of their ability to absorb and store magic inside of them. Sea monsters were affected much more strongly in the past, because of the magic in the water. They seem to have stabilized now, but no one can really be sure because they live so deep down.