I can attest (anecdotally) to what Veks says about racism in Sweden. I was over there a few years ago for a conference with Rotary and pretty much any member of the group who wasn't clearly Anglo-Saxon style Caucasian got everything ranging from simple evil looks to full blown offers of fights when we wandered into the bright lights of Malmo.
I quite like Sweden's setup, but as I understand it there are still a number of issues... and beyond that further issues that mean a direct switch from a US style to a Swedish style wouldn't work.
Obviously the tax rate in Sweden in high. However you cut it, taxes in Sweden are far higher than in the US in both absolute and relative terms, which is what allows it to offer the generous welfare system it has. It's this tax and welfare system that influences nearly all the other "problems" with Sweden. As the tax rates are so high most families require duel bread winners, which on the surface is a good step for women's rights (unless of course someone wants to be a house husband/wife). There's another issue though; despite this dual breadwinners approach women seem to have far more defined "jobs" they can go for as opposed to the US (and UK) and are far less likely to break into the "traditional" male roles. I'll see if I can scrounge up the stats, but I believe it's something like of the top 100 Swedish companies only 2 have women in positions of senior management.
Also due to tax rates there are relatively few small businesses started and owned by Swedes within the country which means a large proportion of the workers are employed by either the large corporations or the government... most of the entrepreneurs end up in either Latvia or Estonia. What that means is the "American Dream" of starting your own company, being your own boss and working your way up is (a lot) harder within Sweden. The lack of a liquid employment market and entrepreneurship also causes some of the issues that lead to the racism described above. The welfare system works because of both the high taxes and high rate of employment (about 74% I believe). In recent years however there has been a high level of immigration from less developed countries (I think Sweden has taken in more Iraqis than any other Western nation), which the system hasn't been able to deal with well. The lack of a small business service sector or the chance to start their own enterprises means they're becoming more of a drain on the system (often through no fault of their own) which in turn leads to the resentment.
Statistically Sweden has some of the worst crime rates in the developed world, although that's partly down to the way they report their stats to the UN and Interpol. Even so, the crime rate appears to be roughly comparable to the US and nowhere near the levels of Japan or other "low crime rate" countries. Immigrants are vastly over-represented in the stats... partly tying in with what's seen above.
It's also worth noting that a lot of Sweden's success can be attributed to some great town planning. Public transport is affordable and reliable which means having a car isn't a requisite for working and there are large numbers of small but well made and soundproofed affordable flats for workers (something missing in the US). It's these factors, not just the welfare set up and tax rate, that make the Swedish set up work. Its health system, despite a few flaws, is one of the best in the world by any given indicator and is one of the best examples of single payer (despite small moves towards a hybrid) systems out there.