Wik:
The film was Bogart's last. At the time he was already ill with what would be diagnosed as esophageal cancer. Occasionally unable to be heard in some takes, some of his lines are reported to have been dubbed in post-production by Paul Frees, who also appears in the film as a priest.
Can anyone tell any specific lines that were dubbed in?
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I think it is just a rumor, nothing more. I think all lines were actually voiced by Bogart, whether during shooting or post-production. Maybe the rumor started because Bogart sounds a bit different during certain parts of the movie. When he says his first lines in Feldman's Gym, his voice has more "gravel" in it then in several scenes when he speaks with Toro. However, I think this is because Bogart was speaking in a soft voice in these scenes. Less stress on the vocal chords, which probably had nodules on them caused by heavy smoking, less gravelly voice. Also, it is possible Bogart later dubbed these lines in because his words were muted by other noises and he had a fresher voice then during shooting. Bogart's voice is at it's worst (from a phonological point of view) when he yells at Benko, because he no longer had the lung capacity to yell, that's why his yelling sounds "spitty".
The priest, in my opinion, has an entirely different voice.
None of Bogart's dialogue was dubbed by someone else.
Paul Frees was known as "the man of a thousand voices" because of his facility with accents, intonations, and so forth. He dubbed countless voices in scores of films over the years, often two or more in the same film -- even the same scene. (For a very few examples, you can hear him in such films as Gigi, Operation Petticoat, Atlantis the Lost Continent, In Cold Blood, among many, many others.) He also dubbed a lot of foreign actors into English -- when the Japanese war film Storm Over the Pacific was recut and released in America as I Bombed Pearl Harbor, Frees dubbed every male character's voice! But once you get to know his voice you can always tell when it's him. He definitely did not loop over Bogart, or anyone else in this film, nor did anyone else. Bogie's voice was all his own.
Remember also that, although The Harder They Fall was released in 1956, most if not all of this movie was actually shot in 1955. Bogart didn't really begin to fall ill until the early part of 1956, when he had to abort his next film project (co-starring his wife, Lauren Bacall) when his cancer required surgery, after which he spent the rest of 1956 slowly dying. So when this movie was in production, Bogart was still well enough to do his own lines. In fact, off hand I can't think of a single instance where Bogart's voice was dubbed by someone else, which was something that was not at all unusual back then, even for top stars.