As Carisi is asking Lily's parents about her password, he asks about her cat's name...but it's impossible to input that on an iPad's numerical password screen (which is what appears when he shows her parents). Not a goof: the numbers on a password screen can be used the same as the letters on a telephone keypad. For instance, "cat" can be typed as "228" for a password (or "5459" for "Lily").
When Olivia is searching for Noah at the playground she finds him on the ground with other kids. When she nears the tree across from where he is there was no one standing there. The scene quickly loops and now there is a man leaning against the tree. Not a goof: the tree is large enough to hide a grown man from the angle Olivia approaches.
In the beginning, when examining the body of the young girl, the forensic mentions DNA under the fingernails AND semen on the girl's thigh, this and the fact that the girls clothes had been torn. In the end, when the man guilty was interrogated, he mentions holding over her mouth and shaking her in the back of his van, causing her head to bump against the floor and her passing out. But no one mentioned the semen found on the girl. Not a goof: the officers get a confession about the death (the most important aspect). The interrogation is not necessarily over when Olivia gets up from the table.