MTV has come under fire for being to sensitive by censoring too much of their programming. They have often altered or removed shows from the channel's schedule. A case of this is was the show 'Beavis and Butt-head', in wake of a child burning down his house after allegedly watching the show, producers moved it from it's 7p.m slot to a late-night 11p.m slot.
In the 1980's the PMRC criticised MTV over music videos that 'supposedly' had explicit imagery of satanism. Since then MTV have developed a strict policy on refusal to air an videos that depict anti-religious bigotry.
MTV also heavily edit a number of music videos to remove references to; drugs, sex, violence, weapons, racism, homophobia and advertising whilst completely removing swear words. A few examples of this are 'Michael Jackson' - "They Don't Care About Us", 'Lady Gaga' - "Poker Face" and 'Maroon 5' - "This Love" etc.
For a company with so much power and funding, they seem to be very weak. Music is an art that is expressed which MTV doesn't seem to embrace. Despite them being massive, there are several case of them giving in to pressure from the public or certain groups such as the PMRC.