- The union asks for workers to be paid above market rate. The company, of course, has limited resources. So the company agrees to pay union members more, but at the expense of newly hired workers, who aren't in the union and so don't get a vote. The end result is that, after a few decades of this, pay is based entirely on seniority and no one has a reason to do good work.
- The union asks for more benefits. The company, again, has limited resources. So the company and the union agree to lavish retirement plans, which will only have high costs decades later, after the majority of current workers have retired. When the company goes bankrupt and restructures retirement, the newer workers get screwed, but they weren't working there at the time and so didn't get to vote on it. The management who agreed to the expensive plans is sitting pretty, despite having bankrupted the company, since they are typically older and are now retired too.
- A lousy worker's vote counts just as much as a good one's. On the other hand, a good worker who might replace the lousy worker isn't employed at that company, and so doesn't get a vote. Hence, the union gradually creates protections that make current workers almost impossible to fire, while good workers who might replace them remain out of a job.
(Examples available ad nauseam.)
It's what you'd expect from democracy, really - if you give the vote to everyone in a group and nobody outside, that group will enrich itself at the expense of everyone not currently in it. (This is, I suspect, why most Western countries have such horrible immigration policies.)
If Sweden's found a way to fix these problems while still having unions, that's great, but I don't think Americans have yet.
EDIT: There are American unions, like the Screen Actors Guild, that seem like exceptions to this. However, actors don't work for the same company for 45 years, which you'd expect to make all the above problems much less bad.