The main health problem with high fructose corn syrup (HFCS) is that unlike sucrose or glucose, fructose does not trigger an insulin response and thus there is no feeling of satiety ("fullness") when eating products made with HFCS. This means people tend to eat more of something made with HFCS than would have if they had eaten the exact same product made with sugar.
Of course, this same downside applies to naturally occurring sources of fructose, such as fruits, but you would have to eat a large number of apples or grapes to get the same amount of fructose as is found in a candy bar made with HFCS.
The cruel irony is that HFCS is actually significantly more energy intensive to produce than regular sugar. In a rational market, HFCS would either not exist or only be used in specialized circumstances. However, massive corn subsidies in the United States mean that corn is so cheap that HFCS becomes the cheaper alternative than sugar, even though it costs much more energy to produce.