When the file of John McGarrett is shown, his birthday is shown to be 26th July 1948 however, in previous episodes, it has been seen on his gravestone that his birthday was 15th March 1942. This birthday, unlike the one in the file, fits in with the timeline that his father, Steven McGarrett, died in 1941.
When the coma patient/witness on a ventilator was transported, the nurse in charge did not bring an Ambu Bag (manual ventilator) in case of power failure. A nurse would not make that mistake.
In one of the scenes, Danny's ex-captain mentions that it's the first time he met McGarrett. However, in the Pilot episode, Steve mentions that he talked to the captain.
In the Pilot episode, Danny is seen taking Grace to school right before going to the crime scene in the morning. However, this episode mentions that he went to the scene right after the disappearance of the witness.