The Twins have almost never had a good DH, so talking about how their DH options last year sucked isn't saying that much.
The Twins, perhaps like many AL teams, don't think of the DH as a position to fill with the best bat they can find. DH is viewed as as afterthought. Until the Twins treat the DH as a legitimate position just like all the other positions, it will continue being a spot in the batting order to slot people in to "give players a bit of rest."
This is, of course, the wrong approach. The Twins changing their thinking on DH would probably have more of an impact than fiddling around with openers or whatever.
I want them to change their thinking on all the positions, DH included. I want them to put the best possible offense together and let the positional aspect be malleable. I'd find it preferable to keep DH and possibly 1B fluid so as to help cover up any defensive deficiencies, but if they actually find one of those best possible bats and he happens to only fill the DH spot, so be it. But it better be a dang good bat. I don't want some league average guy there which forces the team to go with a below league average guy at another position.