The effect is easily noticeable only for high frequencies, where the wavelengths are no bigger than a few meters.
For the lower frequencies used by AM broadcasting, where the wavelengths are up to hundreds of meters or kilometers, and you use small antennas for reception, it is unlikely to have problems caused by multipath propagation (because the waves will go around obstacles instead of being reflected; only for the higher frequencies of the shortwave range you can have multipath reception of signals reflected by the ionosphere, but the objects that are around the receiver still do not cause problems).
When there is multipath propagation, you would not hear echos, because the time difference between the different paths is too small, due to the high speed of the radio waves. What you get is interference between the multiple signals, which can reduce too much the strength of the received signal. When the signal is reflected on some paths by mobile objects, or when the receiver itself is moving, the received combined signal will have an amplitude that varies in time, with intervals when the signal cannot be received (i.e. fading).
For the lower frequencies used by AM broadcasting, where the wavelengths are up to hundreds of meters or kilometers, and you use small antennas for reception, it is unlikely to have problems caused by multipath propagation (because the waves will go around obstacles instead of being reflected; only for the higher frequencies of the shortwave range you can have multipath reception of signals reflected by the ionosphere, but the objects that are around the receiver still do not cause problems).
When there is multipath propagation, you would not hear echos, because the time difference between the different paths is too small, due to the high speed of the radio waves. What you get is interference between the multiple signals, which can reduce too much the strength of the received signal. When the signal is reflected on some paths by mobile objects, or when the receiver itself is moving, the received combined signal will have an amplitude that varies in time, with intervals when the signal cannot be received (i.e. fading).