The inductor has got parasitic capacitance that forms a resonant circuit at a high frequency. The action of switching current into it and turning it off ALWAYS causes this to happen on pretty much ALL power supplies of this type. The leakage capacitance of the series MOSFET also interacts with the inductance to modify this too.
The inductor is 27uH and maybe the MOSFET has 200pF D-S capacitance - this would cause a resonant frequency of: -
f = \$\dfrac{1}{2\pi\sqrt{LC}}\$ = 2.16 MHz
OK I'm just guessing at what \$C_{DS}\$ is but it's definitely in the same ballpark as you figures. You don't need to add a snubber - doing so will reduce the efficiency of your circuit and what are you trying to "protect" against?
First I'd suggest you to double check your power requirements. You are consuming 12+2.5 = 14.5 watts of power which seems too much for a home automation product. If you are just running some relays, micro-controllers and sensors on that power, you are probably doing it wrong. Again, you might be running some extra load on it and it might be correct.
Now coming to your hardware selection, there are a few questions that you need to answer first:
1) Are there any physical constraints on size of the power supply?
2) Are you going for a bulk production?
3) Do you have some knowledge about electronics and are you willing to put some time in R&D?
If your answers are mostly "NO", then simplest thing would be to go for a transformer based power supply. You can choose a center tap transformer or two different transformers - One for 12V and other one for 5V. Add two linear regulators 7812 and 7805 to make things more robust and you are done. Obvious cons will be high cost and bigger physical size but it will get you up and running very fast. Alternatively you can just buy two power adapters.
However if your answers are mostly "YES"(which is the case actually), then I'd suggest you to go for switching power supplies. Why? Low cost, smaller size and higher efficiency. In the cost of one normal transformer, you will have complete power supply designed if you choose your part vendors wisely. If all major companies are giving you an SMPS based chargers, there must be a good reason to it. If you have decided to go for this, these are the points you need to research on:
1) Selection of an offline switcher IC. You need to choose an IC suitable for your power requirements. For ex - Viper22a is one of the commonly available ICs and it can give you around 20 watts of power if your input voltage is in the range 195V to 265V.
2) Selection/design of the ferrite core transformer - This is the toughest part in my opinion unless you have a good knowledge about magnetics. A cost saving idea would be to go for multiple secondary windings - dual to be precise. One for 12V and the other one for 5V. You need to select a suitable transformer core for the power requirements. You can follow app notes for this purpose.
3) Once these two key components have been selected, you need to pay some attention to noise. What's the max ripple noise you can accept? If you aren't performing any precise adc measurements, 5-10% of output voltage is usually acceptable. For analog stuff, you need rock solid power supply or you will end up introducing some measurement error. Once the acceptable noise has been agreed upon, you need to design a suitable filter for the same. In some cases, just a capacitor is enough. In other cases, an LC filter might be required.
Note: There is yet another cheaper version - Non isolated power supply where you use an inductor rather than a flyback transformer. However you are always at a risk of shock if someone touches the circuit and usually not recommended.
Best Answer
Check for breaks in traces or lifted pads, check the output filter capacitor ESR (probably a prime suspect), and the current sense resistor (source resistor on the MOSFET) value.