Evander’s Additions: 

Honkosecond – “the time between when the traffic light changes and the person behind you in L.A. honks his horn.”  The Honkosecond is “the smallest measure known to science” Qtd in Robert Levine, A Geography of Time (1997), pg 152.

Blatantly copy-pasted from Wikipedia

Friedman

The Friedman is approximately six months, specifically six months in the future, and named after columnist Thomas Friedman who repeatedly used the span in reference to when a determination of Iraq’s future could be surmised.^{[30][31][32][33][34][35][36]}

Jiffy

A jiffy is a unit of time used in computer operating systems, being the interval of time between system timer interrupts. This interval varies from system to system, but is typically between 1 and 10 milliseconds.

Microcentury

According to Gian-Carlo Rota,^[37] the mathematician John von Neumann used the term microcentury to denote the maximum length of a lecture. One microcentury is 52 minutes and 35.7 seconds – one millionth of a century.

Mooch

A period of approximately 10 days, named for former White House Communications Director Anthony Scaramucci‘s famously short tenure. The name “Mooch” coming from a nickname for Scaramucci, “The Mooch.”^{[citation needed]}

Nanocentury

A unit sometimes used in computing, the term is believed to have been coined by IBM in 1969 from the design objective “never to let the user wait more than a few nanocenturies for a response”.^[38] A nanocentury is one-billionth of a century or approximately 3.156 seconds. Tom Duff is cited as saying that, to within half a percent, a nanocentury is π seconds.^[39]

Tatum

A tatum is the “lowest regular pulse train that a listener intuitively infers from the timing of perceived musical events.” It is named after the legendary jazz pianist Art Tatum.^[40]

Shake

In nuclear physics, a shake is 10 nanoseconds, the approximate time for a generation within a nuclear chain reaction. The term comes from the expression “two shakes of a lamb’s tail”, meaning quickly.^[41]

New York Second

The New York Second (“the shortest unit of time in the multiverse”) is defined as the period of time between the traffic lights turning green and the cab behind you honking.^[42] The idiomatic expression “in a New York minute“, used in various contexts to mean an instant or a very short time, is of similar origin, referring to the busyness of New York and impatience of its residents.