Sensitive electronics like computers and TV's use power supplies. Those power supplies take the household voltage and convert it to filtered DC, which is then used to power the circuitry. It's even inverted back to AC to power the TV illumination. Those power supplies often have a floating ground and will quite often accept power from 50 to 70HZ and 90 volts to 250 volts without any issue. If I were to guess, your screen issues are not related to dirty power. However, they could be related to power spikes or surges such as lightning.
Computer UPS's on the other hand, can be quite intolerant of frequency and voltage swings. Any time my power is substandard, the various UPS' in my home beep their alerts.
I suggest having a good UPS on your TV and cable/sat box for the protection against surges and unnecessary outages. Both can be damaging.