Martin Luther's opposition to the authority of the pope and his questioning of the doctrine of salvation were considered heresy. On which of these issues did Luther agree with the Catholic Church?

You didn't offer a list of issues to choose from, so let me offer my own answer.

Luther and the Catholic Church both agreed on who God is and the Bible's account of Christ's life.

In Martin Luther's own confession of faith known as "The Smalcald Articles," written in 1537, Luther summed up the things where his side and the Catholic side were in agreement:

That Father, Son, and Holy Ghost, three distinct persons in one divine essence and nature, are one God, who has created heaven and earth. That the Father is begotten of no one; the Son of the Father; the Holy Ghost proceeds from Father and Son. That not the Father nor the Holy Ghost but the Son became man. That the Son became man in this manner, that He was conceived, without the cooperation of man, by the Holy Ghost, and was born of the pure, holy [and always] Virgin Mary. Afterwards He suffered, died, was buried, descended to hell, rose from the dead, ascended to heaven, sits at the right hand of God, will come to judge the quick and the dead, etc., as the Creed of the Apostles, as well as that of St. Athanasius, and the Catechism in common use for children, teach.

Concerning those articles of faith, Luther wrote, "there is no contention or dispute, since we on both sides confess them."

The remainder of Luther's Smalcald Articles went on to detail the many ways in which his confession differed from the teachings of the Roman Church, especially in regard to the doctrine of salvation and the authority of the pope (as you mentioned in your question).