Following the knock-out gas attack, IRA operations show up in scuba gear. They're not using oxygen masks, so they would have passed out in the same manner.
Casey drives Costigan away from a payoff for someone threatening to turn him in, but in the next shot, Costigan is driving, and Casey is in the passenger seat. However, she had stopped the van after the explosion, and when she is shown in the passenger seat, she's sobbing quite heavily. It's easy to infer she was no longer able to drive and they swapped seats while the van was stopped.
The sound from the Twin Huey (UH-1) helicopter heard at the beginning was actually dubbed over sound from a Hughes/MD 500 (model 369) helicopter.
The sound from the Coast Guard helicopter was actually sound dubbed over from a Bell 47.
When Danny walks into McGarrett's office he tells him to look at page six of the newspaper. He opens the paper and looks at the right hand side of it (complete with a shot of his right hand thumb in the picture). This would be an odd numbered page, presumably page seven.