While his early research established him as a formidable scholar and skillful fieldwork supervisor in the province of North American Plains archaeology, he is best known for his studies of Polynesian prehistory, especially his investigations into the production, transportation and erection of the monumental statuary on Rapa Nui (Easter Island) known as moai.

On the occasions of his childhood visits to her home in Mesa, Arizona, she would drive him to the town dump where he spent days at a time conducting his own stratification studies and enthusiastically reporting his results to her family at suppertime.

After World War II ended, Mulloy returned to graduate studies in Chicago with his wife, Emily, and their infant daughter Kathy, who was born in 1945.

Apart from Professor Frison, Mulloy's former students at the University of Wyoming include former US Senator from Wyoming, Alan K. Simpson; Charles Love, a geologist on the faculty of Western Wyoming College and a researcher in Rapa Nui Geology and Archaeology; Dr. Dennis J. Stanford, Chair of the Department of Anthropology of the National Museum of Natural History at the Smithsonian Institution in Washington DC; and Sergio Rapu Haoa, former director of the anthropological museum on Rapa Nui and the island's first native governor.

Named for James Allen of Cody, Wyoming, who brought the location to Mulloy’s attention in 1949, the site yielded a class of long, parallel-sided, unstemmed, concave-based projectile points used by paleo-Indians to hunt Bison occidentalis during the Pleistocene era.

In 1955, following his famous Kon-Tiki Expedition (1947), the Norwegian explorer Thor Heyerdahl assembled a team of specialists to conduct archaeological research at various sites throughout Eastern Polynesia.

The international research staff that Heyerdahl brought together subsequently published the results of their investigations in Volume I of Archaeology of Easter Island (1961).

Shortly after his initial survey of Rapa Nui, Mulloy recognized the tremendously rich archaeological character of the island, its significance for understanding Oceanic prehistory and its potential to become an outstanding open-air museum of Polynesian culture.

Mulloy later edited and translated a series of radio-broadcast lectures on Rapa Nui ethnology and prehistory that Padre Sebastián had originally prepared for Chilean naval personnel stationed in Antarctica.

In 1978, in recognition of his distinguished and unselfish work on behalf of the Rapa Nui community, Mulloy was named Illustrious Citizen of Easter Island, by then mayor Juan Edmunds Rapahango.

Earlier that year, the Chilean government had bestowed upon him their highest civilian honor, the Orden de Don Bernardo O'Higgins.

His widow, Emily Ross Mulloy, his son Patrick, his daughter Brigid and his grandson Phineas Kelly were present.

Colleagues and friends joined the Rapa Nui community in paying their respects to the man whose work had brought their island to the attention of the world.

In 2003, twenty-five years after his death, the College of Arts and Sciences at the University of Wyoming named him to their roster of Outstanding Former Faculty.

Mulloy's personal library forms the core of a research collection now located on Rapa Nui at the Father Sebastian Englert Anthropological Museum.