I think most people think that if the Twins are going to improve their offense and team defense it is going to have to be in the infield. Morneau is obviously set at first and Casilla gave every indication that he is going to be the second baseman and number two hitter. Some fans have suggested moving Casilla to shortstop, but it doesn't look like the Twins are interested in that idea.
So the left side of the infield is really where improvement can be expected. Punto is a free agent, but the Twins are expected to try to resign him. Buscher and Harris were the other two infielders who played most of the year. You can add Tolbert to that mix.
The minor leagues do not have a lot of players who appear ready. Trevor Plouffe is a shortstop and was a first round pick in the draft. But he is young and appears at least a year away. The Twins also have re-signed Alexander Machado, a guy they took in the Rule 5 draft a couple years ago who has been injured the last couple years. He hit well at AAA last year, but he has only played second base since his arm injury. If Punto isn't re-signed, Machado may get a shot at the utility player role, but he is more likely AAA roster filler along with Matt Macri.
There are two different needs here. Punto, if re-signed, is a good defensive shortstop and he had enough bat this last year to hold down the position. Compared to Punto, Harris is bit of a defensive liability at shortstop. He can play the position, but you probably don't want him out there every day. He will need to hit better to hold down a spot anywhere. Buscher's problem is also his glove. If he played gold glove defense, his bat would be enough. But he does not come close. Tolbert is probably not an everyday shortstop and is most likely a utility player. They aren't likely to bring Everett back again, but if they can't sign Punto that may be a possibility.
The opportunities for improvement here are more offense from both shortstop and third base and better defense from third base. I think it is important to remember that whoever plays these two positions they are likely to be the 7th and 8th batters in the lineup. The Twins have Kubel, Young and Cuddyer who can bat in the 5th and 6th spots. Its hard to imagine them picking up a third baseman who is going to be an improvement, much less a shortstop.