How would Biblical Inerrantists resolve perceived tensions between 2 Timothy 3:16 and Hebrews 7:18?

When considering the context of the passage you quoted from Hebrews, one will notice that the the passage is given within a broad discussion spanning several chapters. The focus of the discussion is the contrast between the Levitical Priesthood and the priesthood of Christ. This verse in particular points out that the regulation by which authority is dispensed to the priests is weak and useless. It is not a statement about the Old Scriptures. Consider this commentary by Charles Ellicot,

The intimate connection between these two verses is obscured by the ordinary translation. They point out with greater fulness and clearness what is involved in the statement of Hebrews 7:16. “For there is an annulling of a preceding commandment, because of its weakness and unprofitableness (for the Law made nothing perfect), and a bringing in thereupon of a better hope, by which we draw nigh unto God.” (It must be borne in mind throughout that by the “commandment” is meant the ordinance which created the Levitical priesthood, not the Law in general.) That Jesus was not made Priest according to a law of a carnal commandment (Hebrews 7:16) involves the annulling of that commandment; in His becoming Priest according to a power of indissoluble life is involved the introduction of a better hope. This is the general meaning, but each division of the thought is expanded. The appointment of a different priest by the very authority on which the former commandment rested, the divine decree, showed that commandment to be of force no longer: as we have already seen (Hebrews 7:11), this is because the commandment is weak and unprofitable—because the priesthood it creates cannot attain the end of its institution, which is to bring men into fellowship with God.

Let us then consider the immediate context of the passage.

Hebrews 7:11-16 (NIV) If perfection could have been attained through the Levitical priesthood—and indeed the law given to the people established that priesthood—why was there still need for another priest to come, one in the order of Melchizedek, not in the order of Aaron? For when the priesthood is changed, the law must be changed also. He of whom these things are said belonged to a different tribe, and no one from that tribe has ever served at the altar. For it is clear that our Lord descended from Judah, and in regard to that tribe Moses said nothing about priests. And what we have said is even more clear if another priest like Melchizedek appears, one who has become a priest not on the basis of a regulation as to his ancestry but on the basis of the power of an indestructible life.

So, the "former regulation" in the verse you cited refers to the process by which the Levitical priests were chosen- by virtue of their ancestral father, Aaron, and his ancestral father Levi. These priests are men who by nature of their flesh are imperfect and are not immune to weakness wrought by the flesh whether the priest is good or bad. Because of their mortal tendencies, these priests, even when fulfilling their duties perfectly, were powerless to bring lasting atonement to their people. The Biblical narrative, however, presents many opportunities to observe very bad priests.

1 Samuel 2:12-16 (NIV) Eli’s sons were scoundrels; they had no regard for the Lord. Now it was the practice of the priests that, whenever any of the people offered a sacrifice, the priest’s servant would come with a three-pronged fork in his hand while the meat was being boiled and would plunge the fork into the pan or kettle or caldron or pot. Whatever the fork brought up the priest would take for himself. This is how they treated all the Israelites who came to Shiloh. But even before the fat was burned, the priest’s servant would come and say to the person who was sacrificing, “Give the priest some meat to roast; he won’t accept boiled meat from you, but only raw.”

If the person said to him, “Let the fat be burned first, and then take whatever you want,” the servant would answer, “No, hand it over now; if you don’t, I’ll take it by force.”

This sin of the young men was very great in the Lord’s sight, for they were treating the Lord’s offering with contempt.

While there were certainly honest Levitical priests who carried out their duties well, the former dispensation was powerless to prevent preists like these. Christ, on the other hand, is not a Priest in the order of Levi, because Levi is not his Father, but Judah is. The priesthood of Christ is not ancestral, and given by the old regulation, but instead by a new regulation. Instead of an oath sworn by a son of Levi, this regulation regarding priesthood is initiated in an oath sworn by God himself regarding his own Son.

Hebrews 7:16-22 And what we have said is even more clear if another priest like Melchizedek appears, one who has become a priest not on the basis of a regulation as to his ancestry but on the basis of the power of an indestructible life. For it is declared:

“You are a priest forever, in the order of Melchizedek.”

The former regulation is set aside because it was weak and useless (for the law made nothing perfect), and a better hope is introduced, by which we draw near to God.

And it was not without an oath! Others became priests without any oath, but he became a priest with an oath when God said to him:

“The Lord has sworn and will not change his mind: ‘You are a priest forever.’”

Because of this oath, Jesus has become the guarantor of a better covenant.

One can see that the passage is contrasting the regulations for dispensation of priestly authority. In closing, consider Matthew Henry's commentary on the verse:

The law which made the Levitical priesthood, showed that the priests were frail, dying creatures, not able to save their own lives, much less could they save the souls of those who came to them. But the High Priest of our profession holds his office by the power of endless life in himself; not only to keep himself alive, but to give spiritual and eternal life to all who rely upon his sacrifice and intercession. The better covenant, of which Jesus was the Surety, is not here contrasted with the covenant of works, by which every transgressor is shut up under the curse. It is distinguished from the Sinai covenant with Israel, and the legal dispensation under which the church so long remained. The better covenant brought the church and every believer into clearer light, more perfect liberty, and more abundant privileges. In the order of Aaron there was a multitude of priests, of high priests one after another; but in the priesthood of Christ there is only one and the same. This is the believer's safety and happiness, that this everlasting High Priest is able to save to the uttermost, in all times, in all cases.