From The additional notes to Charles Spurgeon's The Treasury of David: Psalm 106:
Verse 8. Nevertheless he saved them. If God should not shew mercy to his people with a nevertheless, how should the glory of his mercy appear? If a physician should only cure a man that hath the headache or the toothache; one that hath taken cold, or some small disease; it would not argue any great skill and excellency in the physician. But when a man is nigh unto death, hath one foot in the grave, or is, in the eye of reason, past all recovery; if then the physician cure him, it argues much the skill and excellency of that physician. So now, if God should only cure, and save a people that were less evil and wicked; or that were good indeed, where should the excellence of mercy appear? But when a people shall be drawing near to death, lying bed ridden, as it were, and the Lord out of his free love, for his own name's sake, shall rise, and cure such an unworthy people, this sets out the glory of his mercy. It is said in the verse precedent, "They rebelled at the sea, even at the Red Sea", or, as in the Hebrew, "even in the Red Sea; "when the waters stood like walls on both sides of them; when they saw those walls of waters that never people saw before, and saw the power, the infinite power of God leading them through on dry land; then did they rebel, at the sea, even in the sea; and yet for all this the Lord saved them with a notwithstanding all this. And I say, shall the Lord put forth so much of grace upon a people, that were under the law; and not put forth much more of his grace upon those that are under the gospel?—William Bridge.
As many of these writers point out, Psalm 106's great theme is Nevertheless. It applies not only to God's actions, however, but also man's.