In 2005, the American Jesuit theologian Cardinal Avery Dulles looked forward to the meetings of cardinals before the conclave (called General Congregations) because he thought there would be a high-level discussion of issues facing the church. He was disappointed and bored by the proceedings.
According to the 1996 constitution Universi Dominici Gregis  ("Of the Lord's Whole Flock"), at the first General Congregation, the cardinals are given a copy of the constitution and can raise questions about the meaning and implementation of its rules. The part of the constitution regarding the vacancy of the Apostolic See must also be read aloud. This is 3,500 words of tedious prose, or 3,100 words if they drop the chapter on papal funerals. The cardinals must swear an oath on the Gospels to observe the constitution's rules and to maintain secrecy.
In a subsequent congregations, the cardinals will deal with other boring issues, such as approving expenses incurred between the resignation and election of a new pope and the logistical preparations for the conclave.
They also pick "two ecclesiastics known for their sound doctrine, wisdom and moral authority" who will present to the cardinals two meditations on the problems facing the church and on "the need for careful discernment in choosing the new Pope." The first meditation is given sometime before the conclave while the second is given in the Sistine Chapel right before the first vote.
The most important thing the cardinals will have to decide is when to begin the conclave. The rules call for it beginning 15 days after the death or resignation of the pope, but Benedict revised the rule after his resignation was announced so the cardinals could begin earlier if all the cardinal electors are present. Some cardinals argue that 15 days is unnecessary because there is no papal funeral, but I ask, "What is the hurry?" This is the most important thing the cardinals will ever do in their lives. They should take their time. Sticking to the normal schedule will allow more time for cardinals from outside Rome to get to know each other and to exchange views on who should be pope. Rushing the conclave benefits the current frontrunners and the curial cardinals who already know all the cardinals.
In the past, the General Congregation has only met in the morning. This time, they will also meet in the afternoon so they can get their business done and get into the conclave. This again is a bad idea. Tying up the cardinals in meaningless meetings reduces the time for informal interaction prior to the conclave. It is in these informal meetings that cardinals get to know the candidates.
Rushing the conclave makes it even more likely that if Avery Dulles were still alive, he would again be bored by the General Congregations.
Update 3/5/2013: Apparently the cardinals agreed with me that meeting twice a day was a bad idea and have decided not to meet in the afternoon on Tuesday and Wednesday. On Monday afternoon, Father Raniero Cantalamessa, preacher of the Pontifical Household, gave the Cardinals the first meditation required by the constitution.