Nixon wasn't a notably "corrupt" President, in the sense of obviously perverting the course of Government for personal gain. His Vice President, Spiro Agnew, was more evidently corrupt in that sense. Nixon was well known for his friendship with a group of wealthy men who backed him for all of his long career, but there's little obvious connection to graft- whether we're speaking of Robert Abplanalp or Bebe Rebozo, there's not much suggestion that these men were buying anything in particular. One can compare with Agnew, against whom there were specific charges of soliciting kickbacks from government contractors when he was Baltimore County Executive and later Governor of Maryland.

Nixon had been well known for "dirty tricks" his entire career: in his campaign for Senate in 1950, he famously smeared his opponent Helen Gahagan Douglas, with the famous epithet that she was "pink right down to her underwear", suggesting that she was a communist, together with a statement that had a bit of a lewd tone for the era. His campaign manager described their strategy ""The purpose of an election is not to defeat your opponent, but to destroy him" -- and that reputation stuck with Nixon. This red-baiting style was present from Nixon's first campaign, in 1946 against Jerry Voorhis; anyone paying attention to Nixon would have understood it as his trademark.

When you ask "how informed was the public" -- you have to be more precise: "which public?" "informed" of what, exactly?

His most public brush with a charge of public corruption per se had been during the 1952 campaign, when he was nearly dropped from the ticket because of allegations of improprieties in his use of funds from backers-- this leads to his celebrated "Checkers Speech", which satisfies the Republican Party and Eisenhower. One might observe that sensitivities to public corruption were quite high in the 1950s-- one wonders whether the vicuna coat which brought down Sherman Adams would have attracted any attention today. Nixon's eight years as Vice President, in that substantially touchy environment, didn't attract much notoriety in that regard.

Since that time had run for President in 1960, had run for Governor of California, he was a very familiar face. Anyone who was paying any kind of attention would have known who he was, and if they were old enough, would have known of his reputation. He gets the sobriquet "Tricky Dick" in his 1950 campaign, and the monicker sticks, because it represented well enough what a fair number of people thought of him.

Against that, you have to consider that he won victories in the 1968 and 1972 elections; narrowly in 1968, but massively in 1972. That latter election tells you something -- that after having seen four years of Nixon, his popular vote totals went _up_ from 31 million to 47 million-- and he defeats McGovern by 17 million votes, where he'd defeated Humphrey by only 500,000. (note that the 26th Amendment is in effect for the 1972 election, so vote totals included 18 to 20 year old voters where the 1968 election did not).

See:

SCOBIE, INGRID WINTHER. “Helen Gahagan Douglas and Her 1950 Senate Race with Richard M. Nixon.” Southern California Quarterly, vol. 58, no. 1, 1976, pp. 113–126.

BULLOCK, PAUL. “‘Rabbits and Radicals’ Richard Nixon's 1946 Campaign Against Jerry Voorhis.” Southern California Quarterly, vol. 55, no. 3, 1973, pp. 319–359.

Mattson, Kevin. Just Plain Dick: Richard Nixon*'s* Checkers Speech and the 'Rocking, Socking' Election of 1952 (2012)

Levy, Peter B. (Winter 2013). "Spiro Agnew, the Forgotten Americans and the Rise of the New Right". The Historian. 75 (4): 707–739.