How can congenital heart disease be related to a faulty signal transduction pathway?

Electrical defects: The heart have a mechanical structural function and an electrical function with an intrinsic electrical power generator. Few congenital diseases affect the electrical system and conduction. Example: pre-excitation syndromes- one called wpw- abnormal accessory electrical conduction path between atria and ventricle. Symptoms include tachyarrhythmias, dizziness, shortness of breath and even syncope.

Too complex: There are many types of congenital disease with many different and often unknown causes. So. There is no pat answer to this broad question.

Not likely.: Most congenital cardiac defects are due to multifactorial inheritance and environmental factors such as Folic Acid deficiency. I am not aware of specific studies linking them to a faulty signal transduction pathway, although such mechanisms frequently become the final common pathway of multiple etiological pathogenic factors.