Thanks for the Video, Dave!
Actually, I need to jump in here: The example you show here is a somewhat "low-end" example of recent designs by Fluke / Danaher. This technique of laser trimming through glass is not new (been around since at least late 60's / early 70's) and one of the main problems with what you see here is the fly-ash contamination that results from the laser trim process. That ash deposited on the inside glass is not completely inert, and eventually finds its way back onto the network circuit (light, vibration, static fields etc all promote migration). Let alone the mechanical stress on the substrate when you burn into it with the laser. All of this can show up years down the road as a bit of instability in the instrument if its not calibrated often. This is no longer considered "best practices" in precision measurement circles. A stable circuit is a clean circuit!
Very stable resistor networks are done on a substrate using transparent sapphire, not the white (probably) alumina as shown here. Both materials are in the same "ceramic" family, but sapphire can offer a superior end product with better thermal properties. (Its very expensive to work with though and a pain to cut it apart). If you want the resistor network to remain stable, you -don't- touch it with laser trim, no matter what the substrate. The resistor assembly would be cleaned of -all- contaminates, welded into a shielded light-tight / humidity-proof and vibration proof hermetic metal package, and mounted onto a PC board with something besides that wobbly, cheap SIP technique. That's how we do it for military & aerospace applications anyway.
Watch out for thermals around the pins of that SIP package the in the example shown here. This might be only for high voltage input, but if you were trying to attenuate lower level voltages with any sort of precision, the resistor network would not be mounted on the PC board like that. In general, those pins all need to be at the same temperature for low level signals. It could be they weren't after that, since that ~9M ohm resistor is going to make all sorts of thermal noise on its own.
As another poster pointed out, if you have to trim a resistor network to this level, you're not doing the software right somewhere else, maybe. For the last decade or so we have cheap 32 and 64 bit MCU's to handle calibration duties much easier than this, and it results in a much more stable, reliable product. You want a STABLE resistor divider; trying to hit some cardinal divide ratio is usually not necessary at all if you calibrate in software. Just build the resistor divider very close to what you need, then take care of as much as possible for trimouts during software calibration. We haven't needed to use a precision-trimmed resistor divider in years...kind of obsolete like CD's and cassette tapes. And we build precision test / measurement devices all the time.
Of course if low noise is what you need, then good precision Wire Wound resistors, coupled with a thermocouple for temperature compensation at the controller end, can easily outperform printed or diffused resistors used on front-end attenuators for freqs < 250kHz or so.
Thin / thick film network circuits were used extensively by Beckman Instruments, General Instruments, Bourns and others even back to the mid 50's that I know of. The substrates were on glass, sapphire, alumina and any other hard, temperature stable material. In pre-software days the resistors would be trimmed with abrasive techniques (sand blast, bead blast), water jets, diamond saws, microwave / maser, ultrasonic probe, radiation sources, etc. Generally these were for aerospace & military equipment, and in use for many years before Fluke started selling calibration equipment.