The tissue can be fragile, which is why long-lasting sutures are used. The wound may come apart partially or fully. This is called a "dehiscence." This problem is not painful, but needs surgical correction to avoid a V-shaped cleft in the labial margin.
The labia have an abundant blood supply. It is important for the surgeon to cauterize the vessels at surgery. Even doing so, it is possible for a clot to separate and a small collection of blood to develop within the labia. This is quite painful. Prompt surgical attention is needed to remove the clot and cauterize the vessel.
This area is highly resistant to infection, so that this is rarely a problem.
As in most operations, underresection is much preferable to overresection. It is easy to remove more labial tissue if needed, but impossible to restore it. With prudent resection, such problems can be avoided.