Are there side effects of an angiogram?

Yes. Side effects from the angiogram can be related to the procedure (bleeding or injury to the blood vessels from the catheters used to inject the contrast; embolization of intraluminal plaque or air from the catheter) or a reaction to the contrast (allergic reaction, kidney failure).
Few. To name few allergy to contrast agent irregular heart rhythm hart attack low bp vascular complications etc read the pamphlet from the doctor.