This area heals quite quickly and the risk of infection is small although care should be taken to keep the area clean while the piercing is healing. There is a small risk of the piercing going through a blood vessel and causing excess bleeding, although careful placement by your piercer should avoid this. Irritation from the jewellery rubbing or catching on clothing can be a problem for some especially during the healing period. This however is uncommon for the inner labia and is more common for the outer labia.
In some cases especially if a small gauge ring has been inserted, rough foreplay or catching during sex can cause the piercing to tear or graze. This will heal but can spoil the mood. Never use less that 14gauge or 1.6mm jewellery in this piercing - small rings are best. In rare cases and usually if placed very badly this piercing can lead to soreness during sex and they may need to be removed, this is generally a placement problem.