A pamphlet shows that Vanya is a member of the St Pluvium Chamber Orchestra. 'Pluvium' is the Latin word for rain shower.
Cha-Cha's line about visiting places, meeting people, and killing them is the standard military joke. It's given a little more punch consider the time travelling nature of the job.
When Klaus is giving Luther his motivational speech, he uses the phrase "O Captain, My Captain." This is a poem written by Walt Whitman in 1865 about President Abraham Lincoln after his assassination and became popular again after President John F. Kennedy was assassinated, which is also a part of the plot line here. The poem also appeared in Robin Williams' movie "Dead Poet's Society."
Country music star Conway Twitty's real name was Harold Jenkins.
Cha-Cha's line "We get to visit exotic places, meet new people, and then kill 'em." is remarkably similar to the line in Deadpool (2016) when Wade is discussing his teens with Weasel: "...when I was his age, travelling to exotic places... meeting new and exciting people. And then.. Killing them."