Yes, broadband can be noisy. Plain ol' Annex A covers around 26 kHz to 138 kHz. The various flavours use everything up to 2.2 MHz, over domestic wiring that was never designed or shielded for it.
Not only does ADSL affect nearby stuff, nearby stuff affects ADSL. Keep yer cables separated when you can.
Incidentally, the little squares are how digital TV signals show interference/lack of strength. None of the gradual degradation you get with analogue.