In the 1972 NLCS Johnny Bench CIN-N had 2 Stolen Bases, to set a catcher record that has not been tied nor broken.
Johnny Bench (CIN-N) had a Walk-Off Home Run in Game 1 of the 1973 NLCS.
Rick Cerone hit a Home Run in his first LCS at-bat in 1980.
Jody Davis (CHI-N) in 1984 hit 2 Home Runs to set a catcher record, that has not been broken (although tied).
In the 1996 NLCS Javy Lopez set 5 LCS records (all players): Highest AVG (.542), Most Runs (8), Most Hits (13), Most Doubles (5) and Most Total Bases (24)
Mike Piazza (NYM-N) batted .412 in the 2000 NLCS.
In the 2001 ALCS Jorge Posada had 6 Walks & 7 strikeouts.
Mike Matheny (STL-N) batted .316 in the 2002 NLCS>
In the 2003 NLCS Ivan Rodriguez (FLA-N) had 10 RBI's, which set a new catcher record.
Jason Varitek (BOS-A) in 2004 had an OPS of .926 (OBP .355 & SLG .571) with a .321 AVG.
Yadier Molina (STL-N) in the 2006 NCLS had 2 HRs, 6 RBIs and a .348 Batting Average
Exceptional Fielding Plays
In the 1972 NLCS catcher Manny Sanguillen (PIT-N) called for a pitchout on the batter but the pitcher (Dave Giusti) threw strike three down the middle, freezing the batter, Johnny Bench (CIN-N). (Tidbit provided by Al Yellon, Member of SABR)
Damian Miller (ARI-N) caught all 45 innings in the 2001 NLCS.
In the 2002 NLCS Benito Santiago caught all 45 innings.
Jorge Posada (NY-A) caught all 64 innings in the 2003 ALCS.
Ivan Rodriguez (FLA-N) caught all 64 innings in the 2003 NLCS.
In the 2004 LCS, Mike Matheny (STL-N), Jorge Posada (NY-A) and Jason Varitek (BOS-A) each caught every inning of all 7 games.
Mistakes, Blunders & Errors
In the 1984 Series Don Slaught set a Catcher record for Series Errors with 3 and tied the record for Most Errors in a Game (2) set by Manny Sanguillen on October 6, 1974.
Mike Piazza (NYM-N 1999) tied Don Slaught's Series record.
Pat Borders TOR-A had 3 Passed Balls in the 1992 series, a record not tied nor broken.
Jason Varitek BOS-A tied Pat Borders 1992 LCS record with 3 Passed Balls in the 2004 ALCS.