Then Jesus summoned his twelve disciples and gave them authority over unclean spirits, to cast them out, and to cure every disease and every sickness.  These are the names of the twelve apostles: first, Simon, also known as Peter, and his brother Andrew; James son of Zebedee, and his brother John; Philip and Bartholomew; Thomas and Matthew the tax collector; James son of Alphaeus, and Thaddaeus; Simon the Cananaean, and Judas Iscariot, the one who betrayed him.

The authority to cure and cast out demons is given to the apostles, they do not assume it.  For an example of what happens to those who assume such authority without having been given it read what happens to the sons of Sceva, the high priest (Acts 19.13-20).

Cures and healings would become outward signs that the kingdom of God has come.  But more, so that the message the apostles carried would be received and believed.  "Even if you do not believe me, believe the works I do..." (John 10.38)

The apostles power to cure "every disease and every sickness" vastly exceeded our modern prowess with medical technology.  The spiritual life is seen, then, as being vastly superior to the physical world, though we rightly seek to bring spiritual harmony into the physical world.  Living in the materialistic world that we do, however, do we not mistakenly place technology over soul, technique over spirit?  Being programmed, as it were, by the technological, physical world, we carry the same units of weight and measure into the spiritual life, which fails.

Finally, Jesus obviously knew the heart of Judas.  Yet this does not prevent him from giving Judas the same authority as the others.  Two passages come to mind: "God's sun shines on the bad and the good" and "Do not give pearls to swine."  These passages do not apply here though because Judas is still good.  It is not until Luke 22.3 that "Satan enters into Judas."  We can say, however, that the gifts we have been given are in no way a guarantee of future sanctity.  I think the Church defined as dogma in the Council of Trent that "no person's salvation is assured."  (Even St. Paul wasn't certain he was a member of the Elect - see 1 Corinthians 9.25-27)  We always have the capability of turning away later in life, like Judas perhaps seeking an apparent good, and losing final perseverance in the faith.  We are told "be watchful."