The good news is that Unicef has just published an update to its 2007 report (.pdf) on child well-being in the OECD countries as of 2010 and the USA does not have the worst overall ranking.
The bad news is that the countries with an overall rank lower than the USA are Lithuania, Latvia and Romania, none of which were in the 2007 report. (Australia, Bulgaria, Cyprus, Japan, Malta and New Zealand have not been included in the overall league table of child well-being, as they have data for fewer than 75% of the total number of indicators used.)
Currently the link on the Unicef site to the full report to 2010 is not available but a comprehensive and interactive summary in graphic and statistical form is available.
In 2007, the USA had an overall ranking of number 20, one above the United Kingdom which is in 16th place in the new table. The current ranking is number 26 out of 29. The total is more because data is now available from some countries not included in the overall table previously. Those included Iceland which is now ranked 3 (and first in Health and Safety); Luxembourg at 7 and Slovakia at 24. All of these had higher scores than the USA in all 6 dimensions measured. The USA's best rankings were 23 in "Behavior and Risks" and "Housing and Environment"; the lowest was 27 in "Education".
It should be noted that these data relate to 2010 and the "report cards" for many countries caution about the effects of their economic situation and point to areas where improvements can be made.
There could well be a future effect where economic problems result in lower scores both overall and within each dimension but not necessarily affecting the countries' rankings. Greece (13-25), Italy(8-22) and Spain (5-19) are lower ranked as of 2010. Ireland(9-10) and and Portugal (17-15) improved their ranking if you take account of the 2 countries above them in the 2007 table which were not previously included in the overall table.