By mistake I connected my Flashback X4 to a power supply with reversed polarity. Is it serious?
In this instance, the question concerns a Flashback X4, but this applies to other pedals as well:
Yes, this can be very serious and should be avoided at all costs!
Using a power supply witht reverse polarity risks damaging at the very least the power input regulator but most likely everything in its path. It's possible the power input diode into the pedal will act as a fuse, but there's no reason to take this risk and we can only advise against it in the strongest possible terms.
Before plugging in all of your stomp boxes to the power supply, always be careful to verify all your power cables. Some of them are built to deliver reverse polarity. Check your power supplies as well. Some of them are able to reverse polarity, in all outputs or some of them with a push button. As well, please ensure that your external power supply delivers the required 9 Volts DC with a center negative pin. This is the standard but sometimes, you can find some pedals with reverse polarity. Check well before plug in and you will never damage your pedals.