This episode is Barney's first interaction with his father. The episode is season 6 episode 19 (6x19). Father's Day in 2011 was June 19th (6/19).
John Lithgow and Neil Patrick Harris were both nominated for the Golden Globe Award for Best Actor in a Supporting Role in a TV series in 2010, which Lithgow won for his performance in Dexter.
As part of his test of the group, after his dad died, Marshall grows a soul patch, but there are quite a few episides where it is stated that Marshall can't grow facial hair.
Will Shadley who plays J.J. was in Dirty Sexy Money playing another Jr. In the show he played Brian Darling Jr the son and grandson of a prominent NYC family.