I couldn't watch more than 15 minutes of that. It was too depressing, that midwestern shithole it took place (Wisconsin?). The people were all so fat even by US standards, they brought up animal abuse and nobody was likeable. It's a tragedy of western history that so many Germans in the 19th century got tricked into migrating to the midwest and have rotten away since then there. Probably the worst migration decision to make, aside from maybe those that went to Brazil.
Anyways, some parts of the US have low crime and the prisons are small and quaint. Then you have areas like the southwest and deep south where crime is 10x higher, and gigantic prisons packed with violent offenders. There's one in Louisiana, one of the most crime-ridden states, called Angola that's basically a de facto slave plantation since it's like all black prisoners and they do work outside or prisoner workshops in the heat.
People idolize California as a hip place but the prisons there are some of the worst. Some are run by the Mexican Mafia who can order a hit on you if you look at them wrong. Overcrowded, overwhelmed, no emphasis on liberal rehabilitation policies (although many prisoners maybe can't be rehabilitated)
So yeah, aside from states that border Canada prisons in the US can be awful, and many of the bigger ones don't focus on rehabilitation. Maybe it's a moral failing, maybe they're overwhelmed and underbudget, but it's proven that rehabilitation lowers re-offending rate
tl;dr yes prisons in the US are bad
>Have the legal system always been this broken in the US, or is this a more recent development?
No, drug war caused massive increase in prison population
> Is the situation different from state to state?
Yes, very, but not really their fault, some states have huge populations and organized crime presence.