Capsicum is an extract of the compound in hot peppers that make them hot. As such it has side effects similar to that of eating a bunch of hot peppers.
From WebMD "Side effects can include stomach irritation and upset, sweating, flushing, and runny nose."
That said, technically speaking, any compound that causes the body to heat up will burn more calories, and no, it doesn't target fat cells in particular. However, how much of an effect is questionable.
Ephedra, the active ingredient in the original Metabolife supplement (now referred to as Metabolife 356), enabled weight loss through a similar "heat the body" mechanism. Since there don't appear to be many studies on the efficacy of Capsicum for weight loss, we'll assume here that it has the same efficacy as Ephedra. You're looking at, then an extra .9kg/month loss, or about 2lbs per month.
For the short term, that's great, but there's not much evidence to say that it's a long term solution, nor that the test subjects kept the weight off in the long run.
Frankly, I say save your money and spend it on something more worthwhile. Try logging your food for a while, if you aren't already, to make sure you're eating how much you think you're eating, because too many calories is too many calories, even if all those calories came from lettuce.
If you have been tracking, and you're within your goal for the calories, then I recommend seeing a medical doctor (especially if you're female). Many people (women, especially) are prone to a number of conditions that can make losing weight nearly impossible without medical help. Some of the conditions can lead to even more serious consequences if left unchecked (for example, anovulation, often caused by hormonal imbalances caused by polycystic ovarian syndrome, significantly increases a woman's risk of cancer; and, of course, insulin resistance by any cause very often leads to Type 2 Diabetes). If nothing else, the doctor can refer you to a nutritionist, who can go over your diet and help you improve it even further.
The "quick fixes" are often a waste of money. Even if they're successful now, they won't do you good once you've lost the weight and try to "go off" the supplements. The only thing that will allow you to get to and maintain your goal weight is to make changes that you're willing to stick with for the rest of your life. As the saying goes, "it's a marathon, not a sprint."