While not comprehensive, here’s a short list from Leland Ryken’s Worldly Saints of the contributions and weaknesses of the Puritans.

Contributions of Puritanism
• A God-centered life; all of life is sacred because all of live is lived to God
• God can be seen in small things and big things, ordinary and extraordinary
• Be active and expectant of God working
• The Christian life is practical and must be lived.
• A focus on inner realities and not just external appearances; root issues
• Able to balance things often polarized; head & heart, activism & caution
• Simplicity. A simplicity that exalts, not diminishes

Weaknesses of Puritanism
• An inadequate view of recreation
• Could lead to too many rules or strictness in exactness
• Verbose, too wordy
• Partisan spirit; lack of sensitivity to other groups

This also isn’t comprehensive, but here’s a list of what I see as a few of the reasons why I love the Puritans and what their legacy has been.

Legacy of Puritanism
• Pious evangelical theology.
o Bible governs all of life and leads to communion with God and growing in holiness.
o Spiritual heirs: Isaac Watts, Edwards, Whitefield, Spurgeon, Lloyd Jones
o Westminster Confession & Catechisms, Savoy Declaration, Cambridge Declaration
o Christianity as a religion touching head (knowledge), heart (affections), and hands (practice)
• Its reforming emphasis helped lead to Great Awakening and other revivals.
• The family dynamic in the West.
• In some ways, the formation of the United States—republicanism and democracy.
• America’s early institutions: Harvard, Yale, Princeton.
• Banner of Truth and Puritan literature.

Why I Appreciate the Puritans
• A perspective different than 21st century
• No separation between academy and church; the leading theologians and influencers were pastors
• They thought deeply and felt deeply
• They sit on a doctrine or thought and press out its conclusions
• All theology is practical and all practice is theological
• They wrote amidst hard circumstances; persecution, plague, hiding, sickness, war
• They hold up both the glory of God and communion with God