Piper was branded by Ruiz on her left arm. This is seen in multiple scenes across more than one episode. But then later, after everyone goes to Max Piper suddenly has the brand on her right arm. This is a pretty glaring error to make. It's not like all the random fake tattoos seen on prisoners that might get moved a little here or there. This brand was part of a major plot point and the error continuing over years is truly bizarre.
In real life, Dascha Polanco is only two years younger than Elizabeth Rodriguez, who plays her mother.
The timeline of the show often changes; the first season indicates being set in 2010 (upon entering prison, Piper begs Larry to not watch the latest Mad Men (2007) without her, and Larry is shown the latest episode from season 4, which originally aired in 2010). However, season 5 references the San Bernarndino shootings, which occurred in 2015. This cannot be possible as Piper's prison sentence was for 15 months and only about a year has passed in those five seasons.