Dear Marnee,
Zantrex 3 side effects are identical to those associated with excessive caffeine consumption (Zantrex is primarily marketed as a "proprietary xanthine-based stimulant", but xanthine is simply caffeine).
You may be interested to know that one serving of Zantrex 3 will provide you with more caffeine than you'd obtain from 3 cups of coffee -- so caffeine-related side effects may be quite prominent in some people.
It's also important to note that caffeine has many of the side-effects associated with ephedra (nervousness, increased blood pressure, heart palpitations, and so on) and although common in many foods (coffee, chocolate, various soft drinks, etc., etc.) may not be for everyone. It's also possible that because of its high caffeine content, you may experience withdrawal symptoms when you stop taking Zantrex 3.
Also, please recognize that the side effects associated with Zantrex-3 will also be common to other caffeine-based fat burners -- which is to say the vast majority of the products featured on this site.