>Anomaly: The unexpected performance of intended function.
Good or bad, major or minor, an anomaly is when reality does not meet engineering design and expectation. It just happens that in spaceflight the most active time is the most dangerous time and most anomalies result in fireballs when your engine is lit as there is not much room at all for error.
Old memory from the 80's an engineer mentioned that he went down to the lab and found an unhappy test tech. Guy was testing a new pressure sensor and it wasn't able to make 10,000 full cycles without blowing the diaphragm. Turned out the test setup was shock loading the pressure sensor. He was surprised it was almost passing. The solution was a rate limiting valve in the test setup. There was nothing wrong with the pressure sensor.
There is a great write up from one of the guys that developed the thrusters for the Apollo program. They had problem where you could get layers of frozen oxidizer and fuel in the inside of the nozzle. Which would then go explode and shatter the nozzle. The solution was to operate the thrusters so that didn't happen.
https://www.rferl.org/a/soyuz-rocket-anomaly-to-delay-u-s-sa...
10 years ago the folks putting your reaction wheels together botched it, and now they're acting slightly weird? anomaly.
you charged your batteries too hard for years because you thought "max" was a great setting for your battery chargers, and now they're failing? anomaly.
Strangely enough, yes: the satellite guys use 'anomaly' to describe the (angular) position of a body in its orbit. I've never heard where the term originated in that context.
Incidentally, according to what I was just reading, epicycles in principle can be used to approximate any curve if you pick them appropriately. Choosing them is related to fourier analysis which of course hadn't been developed yet. When you hear about it in grade school, it's presented as this dumb thing that doesn't make sense, but it was really not a terrible solution.
The deadpan delivery really does it.
Check out NASA Core Flight System if you're curious, it's an in-house framework and abstracted OS layer meant to support hard real-time flight systems.