It hopes the film will bolster its argument for new animal welfare legislation, proposed in the Queen's Speech, to be passed before the next General Election.
The copies went out in the paper's Saturday edition.
The shocking scenes were filmed to show that they are still legal. Under present law, which dates back to 1911, inspectors can't take any action until there is concrete evidence of cruelty. All they can do is offer advice, but because there is no threat of legal proceedings, this is often ignored.
The Bill, issued as a draft in July, proposes a duty of care on pet owners that would oblige them to keep animals in appropriate conditions. It would also allow for codes of practice and ban the docking of dogs' tails.
Actress Miranda Richardson, TV presenter Gail Porter and "paranormalist" Uri Geller all shadowed RSPCA inspectors for a day in the documentary.
Gail Porter visited one house where eight cats were kept in cages 24 hours a day, forced to sit in their own excrement. Inspectors visit the house regularly but cannot do anything for the cats because they are fed and watered. Porter said: "I'm gobsmacked. What we need is some form of lever to prevent this problem before it happens. And the Animal Welfare Bill is that lever."
The film was previewed at a special screening in London's West End last week. RSPCA director general Jackie Ballard said: "The 'p' in RSPCA stands for prevention, but sadly we often have to rely on prosecutions. We can only act after cruelty has taken place. That is why we want intervention that has teeth in time to stop it happening."