Before they started streaming their adventures, the group named their team "The S.H.I.T.s" (Super High Intensity Team). However, they decided to rename themselves to something more professional when in game they were meeting with nobles. They eventually decided on "Vox Machina", which is Latin for "Voice Machine" and a nod to their roles as voice actors.
None of the cast expected the show to last more than a few episodes. They thought that the length of the episodes coupled with the purely dialogue based content would be too boring to amass any decent sized fan base.
Critical Role started as a one-off private Pathfinder game for Liam O'Brien's birthday. They had so much fun they continued playing. Word got out, and they were eventually asked by Geek & Sundry to make their game into a weekly show wherein they switched from Pathfinder to 5th edition Dungeons&Dragons.
For campaign one, Taliesin Jaffe often used a "golden snitch" D20, which often rolled a crit. At the end of the campaign, he rolled a 1 and threw the die to Matt, who took possession of it. Unfortunately, the die was stolen from Matt's car and it's whereabouts are unknown. The cast hopes it only rolls 1s for the thief.
Before the fight with Kevdak, Liam and Travis snuck Wil Wheaton into the studio to touch all of Matt's things, in hopes that the Wheaton Dice Curse would help them win. Wil Wheaton is known for rolling critical fails (or lower than average) across multiple D&D games.