To build on Old Twins Cap a bit, I think we look too much at the shortcomings of the Twins pitching staff and not enough at the shortcomings of the Twins offense and mistake-prone play. To grab a recent example -- June 29th's 10th inning loss. At the end of 9 innings the Twins were 1-8 w/RISP and had left six on base. The Twins ranks near the bottom of MLB of OPS w/RISP *(particularly with 2-outs); you cannot expect to consistently win games when you routinely leave baserunners on the bags. Additionally, the Twins seem to make lots mistakes -- not necessarily errors -- think wild pitches, passed balls, dropped fly balls in foul territory, poor baserunning, etc. Specific examples from game #2 of the doubleheader include Jeffers sloppy early-home-run-that-wan't trot that resulted in an out at second, which was immediately followed by the Celestino/Miranda confusion of suicide vs. safety squeeze that eliminated a runner a third. Granted, the Twins won 6-0 so the lost runs are moot, but sloppy play is sloppy play. Also in that game, the Twins were 1-9 w/RISP (so you can win with poor performances w/RISP).
In terms of problems, I think the pitching problems are more solvable than the clutch hitting and mistake-prone play. You can buy your way out of the pitching problems (I don't know the Twins appetite for spending more or trading assets), but poor clutch hitting and mistake-prone play seems like a development problem that likely starts early in the minors and will take years to fix.
To summarize, I agree that Twins have pitching problems, but I think the bigger, and more difficult to solve problems are poor clutch hitting and generally sloppy play. I think these problems have plagued the Twins for years and are at the heart of the 0-`18 playoff streak. Until these problems are resolved, I don't think the Twins can be an elite team.