I have a lot of time, so I start playing with Basketball Reference and searching for not-well known stats and records. This is what I found (just games from 1985-1986 season to 2012-13):
Most Points by a Player without missing a single shot:
Gary Payton (Seattle) against Cleveland in 1995
32 PTS - 13-13 FG - 1-1 3PT - 3-3 FT
http://www.basketball-reference.com/box ... 40CLE.html
Most Points by a Player without missing a single shot in a PO game:
Serge Ibaka (Oklahoma City) against San Antonio in the Conference Finals of 2012
26PTs | 11-11 FG | 0-0 3PT | 4-4 FT
http://www.basketball-reference.com/box ... 20OKC.html
Most Points by a Player without missing a single shot in a Finals game:
Lamar Odom (Los Angeles Lakers) against Boston in 2010
12PTs | 5-5 FG | 1-1 3PT | 1-1 FT
http://www.basketball-reference.com/box ... 80BOS.html
Most Points by a player who only play 1 game in the NBA:
Oliver Lafayette (Boston) against Milwaukee in 2010
7 Points
http://www.basketball-reference.com/box ... 40BOS.html
Most Points by a player only shooting FT
Clint McDaniel (Sacramento) against Milwaukee in 1996
8 Points
http://www.basketball-reference.com/box ... 00MIL.html
Jarron Collins (Utah) against New York in 2005
8 Points
http://www.basketball-reference.com/box ... 30NYK.html
Most Points by a player only shooting 3PT
Robert Horry (Houston) against Cleveland in 1996
27 Pts | 9-12 3PT
http://www.basketball-reference.com/box ... 20CLE.html
Most FG attempts by a player who didn't score
Dino Radja (Boston) against (San Antonio) in 1993
0-14 FG | 0-2 FT
http://www.basketball-reference.com/box ... 60SAS.html
Most Points by a player in the first game of the season
Michael Jordan (Chicago) against (Cleveland) in 1989
54 pts
http://www.basketball-reference.com/box ... 30CHI.html
Most Points by a player in the first game of his carrer
Willie Anderson (San Antonio) against Los Angeles Lakers in 1988
30 pts
http://www.basketball-reference.com/pla ... rwi01.html
Allen Iverson (Philadelphia) agains Milwaukee in 1996
30 pts
http://www.basketball-reference.com/pla ... sal01.html
Lamar Odom (Los Angeles Clippers) against Seattle in 1999
30 pts
http://www.basketball-reference.com/pla ... mla01.html
Most points by a player older than 40 years
Michael Jordan (Washington) against New Jersey in 2003
43 pts
http://www.basketball-reference.com/box ... 10WAS.html
Oldest player in score a double-double
Dikembe Mutombo (Houston) against Golden State in 2009
42 years and 289 days | 10 pts | 15 rebounds
http://www.basketball-reference.com/box ... 00GSW.html
Most points by a player without rebounds, assists, steals, blocks, turnovers or fouls
Michael Redd (Milwaukee) against Houston in 2002
29 pts
http://www.basketball-reference.com/box ... 00MIL.html
Player with more minutes played and wihout points in his carreer
Maurice Baker (Los Angeles Clippers and Portland) in 2005
19 minutes
http://www.basketball-reference.com/pla ... elog/2005/