What problems could occur after aortic valve replacement?

Many: Post op infection , heart block, arrythmias, if its a mechanical valve it will need chronic anticoagulation. There are risks to this as far as bleeding goes. If the anticoag is insufficient the valve can thrombose. If its a tissue valve it has a limited lifespan and may need another follow up surgery.

Relatively safe: Heart surgery is major surgery with lots of potential complications but the good news is that for the vast majority of patients they are uncommon. A lot depends on how well your heart squeezes before surgery and your overall health. With good health and function infection 1%, stroke 1%, irregular heart beat 15-20% (often not serious), death 2% or less. Your surgeon is best resource.