My guess for Jack's death is that the dog is a complete red herring. Upon waking up and realizing the house is on fire (and knowing that Kevin is gone for the night), Jack and Rebecca split up to get the kids out of the house, each taking their favorite child (and as we all know, Kevin is no one's favorite so it's double lucky that he wasn't in that house that night since between his basement bedroom and non-favorite status, Kevin would have been totes dead. Totes). Rebecca gets Randall out but Jack and Kate get trapped. In an attempt to save them, Jack makes a rope out of bedsheets or something, sending Kate down first. She gets down, but accidentally breaks whatever they're using as a ladder, trapping Jack in the fiery house, which is why she blames herself for his death (or by the time she gets out, the fire has reached Jack and he can't make it down). All the emotions around the dog are probably because after Jack's death, the dog is who Kate clings to and after the dog dies, it's hard for her to get another pet.
Also Titanic was released in theaters in December of 1997 but stayed in theaters almost a year, so Randall seeing it on Super Bowl Sunday 1998 is realistic.
And while I'm glad that Kevin got his necklace back, my stomach is turning over the fact that he had to write an apology letter to rapey Charlotte to do it. I mean, what did the letter say, "Sorry I ran out on you after you used me (while I was obviously drunk and emotionally unstable) to fulfill your pathetic high school fantasies?" Ugh!