One place of course is YU Torah Online. Rav Rosensweig teaches at Yeshiva University in New York City and his regular Talmud shiurim are stored at http://www.yutorah.org/. The most direct way to find his shiurim is to go to the Advanced Search page and on the right of the page select him as the Teacher you are looking for and press "Search" -- you will then be taken to a page of over 500 shiurim!
For a more managable selection of his shiurim, which were given to the public, you can also go to Torahweb -- http://www.torahweb.org/. By clicking on Rav Rosensweig's picture on the home page, you will be taken to a list of his essays, as well as a link to audio and video shiurim. If you had time for only one, I would recommend "The Hashkafic Framework of Social Change" recorded in 2003, it is a wonderful description of the uniqueness of the halachic law system and its vitality and ability to face change.
Rav Rosensweig's latest essay on Torahweb can be found here. It is a reflection on the centrality of "Yirat Shamayim As An Approach to Life and As A Legacy."
The final resource that I would recommend is Rav Rosensweig's essay "ELU VA-ELU DIVRE ELOKIM HAYYIM: HALAKHIC PLURALISM AND THEORIES OF CONTROVERSY," which can be found here. He concludes this insightful essay with these words:
Every time I read these closing words I am inspired to study harder and to immerse myself in the sea of Talmud in order to hear one or two notes of the diverse and harmonious symphony that is the halacha.
Finally, it should be stated emphatically that elu va-elu divre Elokim hayyim (these and these are the words of God -- my translation) should never be used as an excuse for complacency or mediocrity. Even as we encounter equal truths we must aspire to pursue our own conviction of ideal truth culled from and on the basis of insights that we form from the wealth of legitimate perspectives that we confront. Our pursuit should be intensified and enhanced by these exposures. In this way we will hopefully emerge with the concept of pluralism beautifully depicted by the Arakh ha-Shulhan in his introduction to Hoshen Mishpat:
"The debates of Tanaim and Amoraim and Geonim in fact represent the truth of the living God. All of their views have merit from a halakhic perspective. In fact, this diversity and range constitute the beauty and splendor of our holy Torah. The entire Torah is called a song whose beauty derives from the interactive diversity of its voices and instruments. One who immerses himself in the sea of Talmud will experience the joy that results from such rich variety."
Torah, then, is to be perceived as a harmonious symphony enriched by the diversity of its instruments and variations and bearing the singular message of devar haShem.