Here are some of the records that were broken, will update the answer if I find out more:
Most saves in a playoff game 1 : 85 by Joonas Korpisalo of CBJ (since shots started being tracked in 55-56 season)
- Note: Some resources award the most saves in a playoff game to Normie Smith, with 90 or 92 saves, who played in net for the Detroit Red Wings in the longest NHL game ever against the Montreal Maroons in 1936. However, this was before shots (and incidentally saves) were officially tracked by the NHL. So Korpisalo holds the official mark of the most saves in a playoff game.
Total combined shots 1 : 151 combined by both teams. CBJ had 63, TBL had 88
Most shots by a team in a game 1 : 88 by TBL (since shots started being tracked in 55-56 season)
Most time on ice 1 : 65:06 by Seth Jones (since ToI has been tracked in 97-98 season)