Indeed, as this Brooklyn Eagle article explains, they rented a gorgeous turn-of-the-century home in Ditmas Park, not all that far from where I once lived (in a modest apartment), and close to--or, potentially part of--the route for my (Not Just) Victorian Flatbush tour.
(The house is on E. 17th Street between Dorchester and Ditmas avenues, and sold for a mere $1.9 million in 2007.)
The Donovan family actually did not live in Ditmas Park/Flatbush during the time depicted in the film--though this neighborhood is understandably a favorite for filmmakers and TV producers because it offers grand houses, reasonable space for street parking, and a lower density of neighbors who might get annoyed.
According to Philip J. Bigger's biography Negotiator: The Life and Career of James B. Donovan, by 1957, five years before the exchange of prisoners, the Donovans had moved from a freestanding home in Bay Ridge, in southwest Brooklyn, "to a fifteen-room, bi-level apartment at 35 Prospect Park West... overlooking Prospect Park."
Wowza. As described on Streeteasy, "designed by the architect Emory Roth, 35 Prospect Park West is a white-glove co-op building with a full maintenance staff and private basement storage for each unit. The 1929 building is home to 74 units over 18 stories, comprised of single floor two bedrooms and spacious duplex four and five bedrooms."
It's located (map) between Montgomery Place and Garfield Place--and on the routes for my Brooklyn 101, Brooklyn 202, and Park Slope tours. In case you're wondering, a 9-room duplex there sold for more than $5 million in 2008. So it's an even more impressive piece of real estate than the one they used for filming. Also, I'm sure there would be way more hurdles for anyone attempting to film there.
The Brooklyn Eagle article, by the way, notes that the film was also shot in the Brooklyn neighborhoods of DUMBO and Brooklyn Heights.