If the question was targeting also the susceptibility to external noise, than the answer accepted was not complete. There is much more involved here.
I can recommend an excellent book on the subject, The Circuit Designers Companion.
You will want to read at least the first two chapters, grounding and wiring.
Decoupling capacitors have their role in reducing the electrical noise radiated out by the circuit. Narrow but possibly high current power supply peaks are contained within the small area near the high speed components, instead of pulling the current all the way from the power supply.
However, if the question was also how to prevent the EMI (Electromagnetic Interference) from the outside to play havoc with your circuit, that there are many other factors involved.
One of the most important things you should take care of is the cable and signal routing. The ground references should be kept separated, and if you had several circuits boards their grounds should be connected in s single point (star topology grounding).
High speed or high current lines should be kept separated from the low level signal lines. If such cables (or PCB traces) have to cross their paths, it should be done at right angle, minimizing the length of path running in parallel, and forming a stray capacitance.
Analog and digital inputs should be protected by filter components, and protection diodes. Output components switching high currents with inductive loads should also be protected by schottky diodes and filter components. Very often the software plays important role. For example, some communication protocols can adjust the signal slew rate (signal edge rise / fall time) to reduce the radiated interference.
There are many other measures, besides obvious shielding, keeping the 'electrically dirty' parts away, orienting the transformer so then it does emit it's magnetic field through the low voltage input stages of some sensitive amplifier. Avoiding or at least keeping the signal path loops short and narrow is always a good practice. Some beginners would route the PCB in a way that there is a power supply (or ground) trace around a board, just in case something needed to be connected. It it is fine if this was a true ground plane, but if it is just a wider track then it should be broken at some point, or it will serve as an antenna (both receiving and transmitting noise). I hope you have the picture, this subject is broad and involves much, much more than spreading few capacitors around the board.
The solution is not to use the wall switch to control the fan, but the remote, as the product is designed; and to produce a wall holder for the remote which is placed such that people coming into the room are guided to use the remote rather than the switch, and such that they can invoke the "light on" function of the remote without removing from the holder, so that the remote acts as the de facto wall-mounted light switch for the room.
The issue is clearly that when you walk into the room, the main switch is always in its expected location, which reinforces the behavior of reaching for it, whereas you have to look for the remote. If the remote is in a holder that is more conveniently reachable than the switch and as easy to operate, that problem will solve itself via user behavior modification.
You could also make modifications to the wall switch to make it less convenient to operate. For instance, if it is a large, flat rocker switch, build a cover for it so that the rocker can only be operated through finger-sized holes in the cover, discouraging regular use.
If these Hunter Fan people were more clever, they would sell or include junction box covers that double as remote control holders. That way users could uninstall their light switch (wiring the circuit so that it is permanently on) and replace the switch panel with the remote control holder panel, so that the remote control now appears exactly where the switch used to be.
You need to decide how the interference is getting to your ADC input. The best way of dealing with the problem is at the source of the problem. The problem could be: -
These are just a few and until you resolve what is wrong and where it is wrong, asking for canonical solutions is premature.
There may be several solutions, all of which will work with any of the pictures in your question and these might involve: -
Work out what is causing the problem first and why.