replacing Judas

Then they returned to Jerusalem from the mount called Olivet, which is near Jerusalem, a Sabbath day's journey away. 13 And when they had entered, they went up to the upper room, where they were staying, Peter and John and James and Andrew, Philip and Thomas, Bartholomew and Matthew, James the son of Alphaeus and Simon the Zealot and Judas the son of James. 14 All these with one accord were devoting themselves to prayer, together with the women and Mary the mother of Jesus, and his brothers.

15 In those days Peter stood up among the brothers (the company of persons was in all about 120) and said, 16 “Brothers, the Scripture had to be fulfilled, which the Holy Spirit spoke beforehand by the mouth of David concerning Judas, who became a guide to those who arrested Jesus. 17 For he was numbered among us and was allotted his share in this ministry.” 18 (Now this man acquired a field with the reward of his wickedness, and falling headlong he burst open in the middle and all his bowels gushed out. 19 And it became known to all the inhabitants of Jerusalem, so that the field was called in their own language Akeldama, that is, Field of Blood.) 20 “For it is written in the Book of Psalms,

“‘May his camp become desolate,

and let there be no one to dwell in it’;

and

“‘Let another take his office.’

21 So one of the men who have accompanied us during all the time that the Lord Jesus went in and out among us, 22 beginning from the baptism of John until the day when he was taken up from us—one of these men must become with us a witness to his resurrection.” 23 And they put forward two, Joseph called Barsabbas, who was also called Justus, and Matthias. 24 And they prayed and said, “You, Lord, who know the hearts of all, show which one of these two you have chosen 25 to take the place in this ministry and apostleship from which Judas turned aside to go to his own place.” 26 And they cast lots for them, and the lot fell on Matthias, and he was numbered with the eleven apostles. (Acts 1:12-26, ESV)

While "waiting" for the Holy Spirit, they weren't idle. They devoted themselves to prayer and appointed a new apostle.

While it would be reasonable to assume that the disciples feelings towards Judas would be a bit raw, Peter recognizes it as (at least part of) the fulfillment of Scripture. Was it Judas' sin. Yes. Was God's plan taking place. Yes.

The criteria for the office of apostle was for someone who had been with them for the duration of Jesus ministry. It is interesting how Peter sees himself and the other apostles - as witnesses of Jesus' resurrection.

Casting lots - they must have been comfortable with the fact that God was in control of seemingly random events.

Justus and Matthias - neither are mentioned again. (Justus possibly mentioned in Acts 15:22). What did they both do - witnessed for Jesus through the power of the Holy Spirit. The official position was important, but didn't define who they were or what they should do. Justus shouldn't be gutted, he should do the job God has for him. Matthias should be complacent, he should do the job God has for him.