Honestly, offensively, there isn't a lot to do. The Twins plan to go with Sano/Park/Plouffe/Mauer at RF/DH/3B/1B has actually been ok. Three of them have OPS+ over 110 and Miguel Sano will hit. Sano's defense isn't great but (to my untrained eye) he looks better now than he did on opening day. He'll never be a great defender but he can play RF until he replaces Joe Mauer at first in a few years. I don't think he defense would be any better at third.
Offensively, the Twins haven't gotten much from LF/CF/2B/SS/C. The answer to LF/CF and 2B are on the 40 man roster. The Twins have 7 OFers 25 or younger on the 40 man roster (Sano, Danny Santana, Oswaldo Arcia, Max Kepler, Byron Buxton, Adam Brett Walker and Eddie Rosario). Dozier is entrenched at second base. The players just have to play better. Dozier looks like he's coming out of the funk and Arcia has been a pleasant surprise. But, basically, our offense isn't going to get better until our young OFers start raking. Buxton and Kepler are starting to hit at AAA and both of them profile as good on-base guys, which the team needs. Rosario might need a demotion. Ideally, Arcia continues to hit well and the Twins can move him and open up a spot for Kepler and Buxton around the all-star break. I don't know what Arcia would bring back but he could be a nice movable piece.
Catcher is a black hole but it's a league wide black hole so the Twins are sort of stuck. Short stop is the one position they might be able to upgrade through a trade. I have no idea what it would cost but Jurickson Profar is putting up good numbers for the Rangers AAA affiliate. He's still young but blocked b/c they are loaded with MI talent. Arcia wouldn't be enough but it does look like they could use some OF help. Maybe a package around Kepler? Other good short stops that are blocked are Yankee's Jorge Mateo and the Astros' Bregman, although I'm not sure the Twins have enough to get either of them.
Pitching wise, the Twins should probably move Phil Hughes to the bullpen, hope Kyle Gibson is healthy and move up the minor league arms as the season goes on. J.O. Chargois, Melotakis and Nick Burdi should all be in the bullpen by the end of the season. Rotation-wise, Ervin Santana is ok, Jose Berrios should stay in, Tyler Duffey should stay in unless/until he gets bombed out. Ricky Nolasco and Gibson have to stay in for now but should be on pretty short leashes. If Meyer puts together a few good starts, he should get an extended run of starts for the Twins at one those guys' expense.
Also, fire Molitor.
Trade candidates - they have a few guys that would bring back nice hauls - Buxton, Sano and Berrios - but those three are probably off limits. After that, the most likely guys to be traded would be Arcia (if he continues to hit), Trevor Plouffe, Kepler (if he continues to put up good numbers at AAA), Park, May and a second round supp pick. If the Twins were willing to eat a bunch of his salary, they may be able to dump Nolasco or exchange him for an equally bad contract. But he's not going to get us anything good.
They could trade Plouffe and bring up Jorge Polanco to play third. His defense would be ok there but he doesn't have Plouffe's power. But he might get on-base a bit.
Unless they put a package around Kepler, none of the trades would be major trades. They might be able to trade for bullpen help or minor league arms that might become Trevor May again. But a package of Kepler, and their tradeable second round pick might bring back something pretty good. Power is tough to get so Arcia and Park might be able to get a back-end starter that's better than Tommy Milone but that's not saying much.
But, basically, this team is a bit light on starting pitching and won't start hitting until some of the guys on the 40 man start hitting. When they do, they'll be good. Pitching is harder to fix so I'd really run Alex Meyer out a half dozen times before I give up on him as a starter.