Would a fetal heart ultrasound find all problems if there were any?

No: No ultrasound can diagnose all problems in a baby, and fetal heart ultrasounds can miss problems too. A good fetal echocardiogram should be able to diagnose most major heart defects in a fetus, but there are factors that can make the exam difficult, like the gestational age of the fetus, the position of the fetus, or a mother who is obese.

Depends.: Depending on maternal bmi, gestational age, number of fetuses, fibroids, fetal position, machine used, duration of the examination, examiner experience and amniotic fluid volume - prenatal sonography can pick up 20-70% of all fetal heart defects. Fetal echocardiography should detect >90% of such defects, but there are not enough pediatric cardiologists interested in fetal echo around to try that.