In March 2013, the FDA released a statement regarding azithromycin products and the risk of QT prolongation (a type of arrythmia). The releases can be seen here: http://www.fda.gov/drugs/drugsafety/ucm341822.htm.
It basically states that azithromycin (Zithromax) is associated with a slight increase in risk of prolonging the QT interval. This risk is higher in those with pre-existing heart conditions.
While there is a risk, it's not all that high. A study published in the New England Journal of Medicine suggested that there are 47 more cardiovascular deaths per one millions patients on azithromycin for a 5 day course of therapy vs amoxicillin. Why not just use amoxicillin then? Many bacteria are resistant to amoxicillin and therefore will not be effective. Azithromycin will usually take care of the infection.
Azithromycin is known as a macrolide antibiotic and it actually is one of the safer medications in that class. Both clarithromycina and erythromycin, two other drugs in the macrolide class, are more likely to cause problems.
Azithromycin is really only recommended to be avoided in patient with pre-existing arrythmias, or patient with low potassium.