The physical phenomenon responsible for blurring of images is the so-called spacial low-pass filtering. When the same phenomenon is applied temporally to sound, sound loses its higher frequency content.
The only legitimate meaning of blurry sound I see then is when there is so much echo or physical obstacles for sound to go around that it loses clarity. Therefore, sound heard in a large echoic chamber (like a concert hall, hangar or cathedral) can be physically blurry, and sound that you hear from behind the wall when someone is speaking there can be blurry as well.
Sound contaminated by interference (like bad radio channel) would be considered noisy, not blurry.
Also, this type of sound would not be considered distorted. Distortion (I'm in danger of getting overly technical here), is a different phenomenon, characterized by non-linear effects, e.g. you speak too loudly into a microphone and it clips, or when you encode audio with very low quality, that's an example of distortion as well. Blurriness would be characterized by linear audio processing, like superposing many reflections (echoes) on top of each other.
I've been an audio processing engineer for some time now, and we rarely use this terminology, it's usually more technical, but I guess blurry would work, and most people in the field would understand it as the same exact phenomenon.