When a window ( = plano parallel plate) is dielectrical coated of has a mirror coating, it is very difficult to tell which side is coated.

One question is : does it matter at all?
The answer is clearly yes!

The coating of a filter usually consists of not just one, but many layers.
For visible light this can be for example 30 layers, but for more challenging filters this could go well beyond 100 layer.

Let us simplyfy to get the idea:
Let’s assume the first layer (first layer reached from light from object side) would reflect light between 420 and 440nm:
The layers 2-30 can assume no 420nm light is contained in the arriving light.

If the filter is mounted reversed so that the 1st coating from above is now the last coating, the original layers 2-30 still assume there is no 420n-440nm light .. but in fact there is.

This wrong orientation causes some light of the wrong wavelengths to arrive for both 0° and 45° incident angle.

If a filter was designed for 0° but is used under 45° incident angle, a lot of unwanted Wvelengths might get through, see Blueshift of bandpass filters

If the filter was designed for 45° Angle and light arrives at 45°, but the filter is mounted reversed, then the reflection does not take place on the first surface of the filter , but instead at the second.
This means the axis of the arriving bundle of light is now shifted by the thickness of the window, times sqrt(2).

As human it’s hard to tell which side of a filter is coated and which isn’t.
There’s a trick however : put the filter on a white piece of paper and look diagonally across the filter. Now the differences are clear to see: