The United States has the most advanced healthcare in the world. Are you referring to healthcare technology, or socialized healthcare? Comparing our railway system is like comparing your highway system to our interstate. Each country is best served by many factors - and our interstate system is highly developed and the main means of travel, both commercial and private.
I would also like you to cite your statistics on all of those claims.
OK, I'll take your points one at a time.
1. Heathcare:
It is probably fair to say that at the top end, the US has the most advanced health care for cutting edge operations of anywhere in the world. Most of Europe isn't exactly far behind here, but sure a lot of new developments still come out of the US. If you have money it is great. I agree. However, I was referring not to those at the top end, but overall. The US spends far more GDP/capita on health care than any country in the world and yet gets overall an inferior system. It doesn't do a lot for a large number of people at the bottom, it is inferior for most and costs much more than a socialised system would. You are getting less than most of the social-European systems and it costs you more. Worst in nearly all respects. (Except at the top I grant you). A little reform and you could probably have the best of both worlds. My goal is not to bash the US, far from it. But to face reality.
This is a well known statistic often quoted in The Economist. But I don't currently have a subscription so I can't access their graphs. However you can see data pertaining to this here:
http://www.nationmaster.com/graph/hea_spe_per_per-health-spending-per-person
Various graphs show varying levels of difference, but all show the US spending the most on healthcare of any country, per capita.
2. Next homicide rates/capita:
These naturally fluctuate from year to year but since the year 2000, the rates of homicide per 100,000 in the US have been: 5.6, 5.7, 5.7, 5.7, 5.5, 5.6, 5.7, 6.1, 5.8, 5.8. I.e between 5.5-6.0
Let's compare that with some averages over the same period for Western European countries:
UK: ~2
France: ~1.6
Germany: ~1
Sweden: ~2.2
Greece: ~0.76
Australia: ~1.45
http://en.wikipedia.org/wiki/List_of_countries_by_murder_rate
Even countries that many US citizens might be scared to visit have lower rates than the US. E.g. Palestine (3-4), Israel (1.87), Côte d'Ivoire (4.07) and some others. Sure there are also plenty of countries much higher on the list as well, but they are not developed, advanced societies like the US. Clearly the US has a violence problem. (Actually a gun problem).
3. Infrastructure:
The US is huge and is not ideally suited to a continental high speed rail network at present. (Maglev technology with speeds upto and over 500km/h though may change that). However along the high density eastern and western seaboards it is very feasible. (I am aware of the Acela express based on the French TGV and plans for highspeed rail in California). Infrastructure like this though requires state subsidy to get built and that lacks in the US. The interstate network in the US as you say is the main means of getting around, (along with flight). But Western Europe and Japan also have highly developed systems at least onpar with that in the US. Again, it is a matter of priorities. Still rather have both though.
4. Incarceration Rates:
The US has the highest levels of incarceration of any country in the world (source:UN see link below), at 737/100,000. Compared to England & Wales at 139/100,000 and Norway at 59. Even China and Russia don't lock up as many people. Somewhere like Denmark only has 3774 people in jail in total. The average in Europe is around 130/100,000. I.e there are 5 times more people in jail in the US on average than in Europe. There are also more Black people in jail in the US than are in higher education. Tell me that isn't a problem.
http://en.wikipedia.org/wiki/Incarceration
http://en.wikipedia.org/wiki/Prisons_in_the_United_States
Whichever category you look at, it isn't very pretty.
One cannot improve if one first does not acknowledge a problem.