1. Keep Justin Wilcox in the fold. Boise State will likely be contacting him about their vacancy, and he'll probably be a finalist along with Bryan Harsin. If he's offered the BSU job, there may not be anything Petersen can do to keep him, but if not he's got to get him locked up and keep Steve Sarkisian from luring Wilcox away. It would go a long way toward keeping continuity with whatever other staff holdovers there may be, current players, and current recruits.
2. Establish recruiting connections, and that starts with retaining Tosh Lupoi. Lupoi holds the key to several players who have already committed to the Huskies, and keeping him on will give the Huskies their best shot at finishing strong this February. If they lose Lupoi in addition to their recruiting coordinator (Peter Sirmon), Keith Heyward, and Sarkisian, they're almost starting from scratch in recruiting with only two months to go.
3. Connect with local high school coaches. Petersen needs a good relationship with Washington's talent if he's going to build a long term winner, so he should be reaching out first and foremost to schools like Bellevue, Skyline, and Lakes.
4. Win the press conference. This isn't ultimately that important in the grand scheme of things -- you'd always rather have a coaches who wins games than press conferences -- but it would go a long way in showing that he's going to be able to deal with the increased media spotlight he's going to be exposed to in Seattle.
5. Fill out the rest of his staff. It will be interesting to see what happens with Marques Tuiasosopo in particular. Does his promotion to interim head coach come with an understanding that he'll be considered for offensive coordinator under Petersen? Or does Petersen have his own guy in mind for that position? I would be somewhat surprised if many other coaches are retained outside of Tui, Wilcox and/or Lupoi, and it will be very interesting to see how Petersen goes about filling the vacancies. He's never really been a destination; at Boise he had to mentor guys and find up and comers. Now, he can get more established coaches if he wants them. Will he raid other Pac-12 assistants?