Referencing the ending of S3E16 "The San Lorenzo Job," Sophie tells Nate, after their night together, he should start using her real name. It is implied he doesn't remember because he was intoxicated. However, in S3E14 "The Ho Ho Ho Job," her Christmas present to him is her real name.
In the ice hole, Parker picks up an electronic device and says that it still had battery, "the cold kept it good". This is a misconception; batteries die off faster at temperatures below the water freezing point.