Electronic – Are there any non-ideal side-effects of putting capacitors in parallel to increase capacitance

Capacitance can be shown to be equal to material permittivity times surface area divided by distance between the plates.

Now for an electrolytic capacitor you have two foil plates with a gel in between to create an insulating layer the manufacturer applies a bias voltage which creates an oxidisation layer.

The important point is that the thickness of this layer is dependant on the applied voltage. The bigger the voltage the wider the layer and the smaller the capacitance.

Several years ago I was advised by am application engineer from NCC (Nippon ChemiCon) that for best life / minimal capacitance drift a capacitor should see between 50% and 75% of its rated voltage in normal use. I have no idea what this is based on but is still a rule of thumb I work to.

If the voltage is too high the insulation layer will widen and capacitance will fall; too low the insulation layer shrinks and capacitance grows.

I have always allowed for ESR doubling over the expected life of an electrolytic capacitor but I design switch mode PSUs so I drive electrolytics quite hard. I have never considered the ESR of an electrolytic given an easy life.

How can a capacitor cause malfunction if capacitance increases? Wouldn't the capacitor simply take longer to fully charge?

Capacitor is a charge reservoir. Switched-mode power supplies need to charge it first. Too large capacitors might make the internal power supply loop go unstable, which would create large voltage deviations across the capacitor and potentially burn it due to too large capacitor heating caused by its non-zero parasitic resistance called "ESR".

Can high capacitance capacitor really cause any sort of "burn"? I mean it cannot store or produce higher current than what is given by power supply, right?

Capacitor do burn quite often. Actually, the aluminum capacitor failure is the most common failure mechanism in large motor drives! Motor drives and other power electronics (solar inverter, wind inverter, car battery charger, ...) exhibit very large current ripples at various frequencies. These ripple currents cause capacitor heating (ESR), which degrades the capacitor capacitance and further increases ESR. It's like a positive feedback. Aluminum caps have limited lifetime measured in thousands of hours. Their lifetime also decreases with elevated temperatures.

The typical way to mitigate this issue is to use multiple parallel caps (splitting the ripple currents) or using higher quality capacitors. These methods, however, tend to increase cost of the final product. The electronics industry is very cutthroat nowadays, which gives rise to designing for full functionality and reasonable failure rate but not a bit more.

Other answers also list good examples of how not only the capacitor can burn but how the large capacitor can cause other components to burn.