These will be premised not on the likelihood of an upset statistically, but on the relative nature of how many people are likely to pick it compared to that statistical probability. (bold is the post-first weekend reactions)
Avoid Kansas or Michigan St. Michigan St would be currently my favored pick if I had to pick someone, but there's a big drop-off and they have been heavily hyped it appears.
There's about an 8 or 9 team draw that makes the most sense to pull from as a title shot.
(In no particular order) Kansas, Michigan St, Oklahoma, Virginia, Carolina, Kentucky, and Villanova, with West Virginia and Purdue being the outside shots (although Virginia playing so slow doesn't help). Of these, Kansas, Michigan State, Carolina and Villanova seem the strongest. Oklahoma's offense isn't as great, Virginia plays too slowly, and Kentucky's defense is pretty meh (they have the top rated offense). (of these teams, 4 are gone, but two were outside shots anyway, only two of the top 7 are, and I avoided Michigan St on account of lots of people had picked them).
2) South Region
Best odds for improvement on the Final Four pick would be to take Villanova or Arizona.
Best odds for upsets:
Arizona losing in the first round - this is mostly the public not liking the play-in game winners. Also the winner of that game (Arizona/Wichita/Vandy) over Miami. (partly right)
Iowa to hold off Temple - this is not an upset, it's just undervalued because Iowa hasn't played well in the Big Ten.
3) West Region
Best odds for Final Four
Most teams here are about priced in correctly. The public seems to have figured out that Oregon was overrated. Oregon may actually be the best "bet", but Oklahoma still seems to be the favorite. Oregon's main weakness is an average defense.
VCU. Oregon St is pretty meh. For some reason this isn't being taken like crazy as a gimme. (duh)
Yale over Baylor - Yale is pretty good. Baylor is a little low for a 5 seed. Yale also looks promising as a rare pick versus Duke (Baylor only looks okay for an upset there). Neither Duke or Baylor has a good defense. (huzzah)
Texas advancing deeper in the field - Elite 8 for example. Northern Iowa is a reasonable upset chance in the first round, but about priced in correctly. After that, Texas is a little underrated. (fortunately didn't take my own advice)
4) East Region
Indiana actually looks slightly favorable here, but mainly taking West Virginia would be useful. (ouch)
Notre Dame losing to Michigan or Tulsa. Notre Dame cannot play defense. (struggled against SFA even)
Pitt or Wisconsin over Xavier. (huzzah)
5) Midwest Region
Virginia or Purdue. Avoid Michigan State if possible
Gonzaga over Seton Hall (and Utah) (huzzah)