[Thanks to SABR's Members & to Retrosheet.org and baseball-reference.com.]

Most errors, career
MLB - 529 - Pop Snyder (1876-1891) 15 seasons
N.L. (19th C.) - 434 - Silver Flint (1878-1889) 12 seasons
N.L. (20th C.) - 320 - Red Dooin (1902-1916) 15 seasons
A.A. - 279 - Pop Snyder (1882-1888) 7 seasons
A.L. - 229 - Oscar Stanage (1909-1925) 13 seasons

Most errors, season
N.L. (19th C.) - 94 - Nat Hicks, New York Mutuals, 45 games, 1876
N.L. (20th C.) - 40 - Red Dooin, Philadelphia, 140 games, 1909
A.A. - 85 - Ed Whiting, Baltimore Orioles, 72 games, 1882
P.L. - 50 - Sy Sutcliffe, Cleveland Infants, 84 games 1890
A.L. - 41 - Oscar Stanage, Detroit Tigers, 141 games, 1911
F.L. - 24 - Art Wilson, Chicago Whales, 132 games, 1914

Fewest errors, season (150 or more games)
N.L. - 4 - Randy Hundley, Chicago, 152 games, 1967
A.L. - 4 - Jim Sundberg, Texas, 150 games, 1979

Fewest errors, season (100 or more games)
A.L. - 0 - Buddy Rosar, Philadelphia, 117 games, 1946
N.L. - 0 - Mike Matheny, St. Louis, 138 games, 2003

Most errors, game (9 innings)
N.L. (19th C.) - 7 - Jack Rowe, Buffalo, May 16, 1883
N.L. (19th C,) - 7 - Dickie Lowe, Detroit, June 26, 1884
N.L. (20th C.) - 4 - Gabby Street, Boston, June 7, 1905
A.A. - 7 - Billy Taylor, Baltimore, May 29, 1886
A.L. - 4 - John Peters, Cleveland, May 16, 1918
A.L. - 4 - Lena Styles, Philadelphia, July 29, 1921
A.L. - 4 - Bill Moore, Boston, September 26, 1927

Most errors, inning
N.L. (19th C.) - 4 - Doggie Miller, St. Louis, May 24, 1895, second inning
N.L. (20th C.) - 3 - Jeff Reed, Montreal, July 28, 1987, seventh inning
A.L. - 3 - Jeff sweeney, New York, July 10, 1912, first inning
A.L. - 3 - John Peters, Cleveland, May 16, 1918, first inning