The serial number on the gun is 1015-59. Not only is this a reference to the recurring 1015, but it is also one day before the original broadcast date of The Twilight Zone: Mr. Denton on Doomsday (1959) (which aired on October 16, 1959), an episode also about a gun that seemed to have a mind of its own.
The funeral service for Jeff Storck's father is held at Cayuga Lake, and Jeff mentions how much his father loved it there. Rod Serling also loved Cayuga Lake and named The Twilight Zone (1959)'s production company, Cayuga Productions, after the lake.
When Jeff Storck walks into the shooting range, the TV in the lobby is showing The Twilight Zone: A Most Unusual Camera (1960). Like this episode, it concerned an inanimate object which was endowed with supernatural properties, in that case a camera. Also, The Twilight Zone: Replay (2019), may be an homage to the classic episode.