I'm about 17 episodes into critical role. I really enjoy it, but binging it can get a tad bit monotonous, so I was thinking about watching them both parallel so I can get caught up on the current game and watch it live. Does the second campaign have spoilers for the first campaign?
Yes, Campaign 2 will spoil parts of Campaign 1
Editor's note: This answer has been somewhat altered from its original version to reflect the later episodes of Campaign 2 that have aired since it was originally posted.
Campaign 2 is set in the same world of Exandria about twenty years after the end of Campaign 1. It mostly takes place on a different continent a long way from the events of C1, and there is no direct connection between the end of C1 and the start of C2; however, some of the events of C1 inform what the world is like in C2, so with knowledge of the world from C2 it's possible to infer a bit about how some events in C1 will turn out when you get to watching them.
In the earlier parts of C2, the stories of the two campaigns are generally well-isolated from each other, though there are sometimes references or callbacks to characters or events from C1 which you may not catch or understand if you're not familiar with C1 and could be considered to be spoilers.
However, later on in C2, some of the important characters from C1 - and some new characters who are closely connected to characters from C1 - start to turn up, which will spoil the fate of certain characters from C1. Despite this, it is a running gag in C2 that the fates of player characters from C1 are never discussed directly in-character, even by the NPCs who know (or should know) them. On at least one occasion, the story of C2 visits a location of significance from C1, albeit only briefly.
The more significant issue that, out-of-character, the cast aren't afraid of occasionally referencing or discussing the events of C1 while playing - and especially in the companion show Talks Machina if you're also intending to keep up with that while watching C2 (which I would personally recommend). There are often jokes and references to later events of C1 which may spoil those events for you if you haven't seen them yet and especially about what happened at the end of the campaign, including pretty major spoilers for how that turns out for some of the characters.
However, I do know someone who kept contemporaneous with C2 while slowly working through watching C1, and it didn't seem to affect his enjoyment of the show negatively.
FWIW, the earlier arcs of C1 are a bit more of a slog as they were still getting to grips with the whole streaming thing and settling in to the format. They get better as time goes on and you'll probably find later episodes are more watchable (in particular you're a few episodes away from a significant change which does tighten stuff up a bit).