He missed birdie putts of 8, 15 and 12 feet on the back nine, along with two par putts from inside 8 feet.
Woods now goes to the North Course to figure out where he is before anyone can get a true sense of how this tournament is shaping up.
"I think he's won here more times than I've won on tour, so I think he knows the place pretty well," Snedeker said. "I think he's very similar to me. He loves putting on these greens. ... We've got three more days to go. There's 155 guys I'm still worried about besides him, so we have a lot more guys to worry about."
Woods played with Rickie Fowler, who had a 77 and was tied for last place.
Mike Weir was among those who had a 66 on the North Course and appeared to be in great shape to make his first cut since 2011.
Mickelson's 72 felt even higher considering he was playing with Snedeker, who was firing at flags and holing his putts. A three-time winner at Torrey Pines, his week began with comments about the amount of taxes he is paying in California, followed by two rounds of apologies for not keeping his opinions to himself.
That wasn't a problem for him Thursday.
"I've been playing better than this, and there's no excuses," Mickelson said. "I've got to get my head a little bit more focused on the shots, and I haven't been as focused starting out. Hopefully, I'll be able to turn that around tomorrow and start a little bit more effectively in the future."