lot of information about this issue at the CDC website. One thing that may have confused many people is that despite there being 'no convincing evidence of harm caused by the low doses of thimerosal in vaccines' it was agreed that thimerosal use should be reduced or eliminated in vaccines as a precautionary measure. A number of countries have done this now, and some countries have now been using vaccines without thimerosal for decades.
This has allowed for some massive studies looking at all sorts of health related issues in children both before and after the use of thimerosal ceased. If this compound was really causing health problems in children we'd see a dramatic change as we stopped its use. However these studies have generally showed little effect and in a number of cases diseases like autism continued to rise in countries after they ceased using this preservative.
The WHO concurs with the CDC in finding no evidence of toxicity from thiomersal in vaccines and no reason on safety grounds to change to more-expensive vaccines.
There are now a massive amount of studies on vaccine safety, particularly the common childhood vaccines. Like all science the results may appear at times to be contradictory and confusing. One way to judge the validity of a website is to consider how it deals with this issue. Both the CDC and WHO websites contain summaries of all the large studies and make a recommendation based on the sum of the evidence.
Other websites, particularly those promoting an an anti-vaccine agenda, tend to cherry pick studies that conform to their view. Science doesn't work that way.