But, it is possible that this is Peter's house. Certainly, the fact that the men took the liberty of breaking through the roof would seem to indicate some degree of propriership, even though going through the roof would not have been difficult. Many houses were flat-roofed and made of wooden beams interwoven with thatch. Removing the thatch would have been relatively easy. This miracle introduces a theme which will become more common in Mark's narrative.
Healing requires faith on the part of the person being healed.
In this case, the response of Jesus was not immediately what was being asked by the paralytic or his friends. Jesus takes the opportunity to go beyond the physical. And this allows Mark to introduce the first of five groups who will oppose Jesus. Here we meet the scribes. As interpreters of the Law, they know that the power to forgive sins belongs to God alone.