Introduced species can be a concern, but usually they don't do too much damage. We often hear only about the ones that DO do damage.
I work in the environmental field--there's a BIG difference between environmental science and environmentalisim--and I have to deal with introduced species ALL THE TIME.
As far as animals, the only ones you see with regularity are:
Norway rats, European starlings, Dogs and cats, and a bunch of other birds the Europeans brought here so they could"feel at home".
Overall, while the populations of these have spread, they have had comparitivly minimal impacts on the environment.
Compared to introduced plants.
Now THERE'S a problem. Privet, Kudzu, I could go on.
Odds are, even if we introduce hundreds of chameleons into hawaii and Florida, the ecosystem will change little.
When a non-native plant comes in, the results can be devastating, since the plants change things literally from the ground up.
Note I'm not condoning or even defending introduction of animal species--no way. However, if we leave the animals alone in Hawaii, I will admit that I am facinated by what may become of them in the next 50 or so years. What kind of phenotypic changes have taken place, are they still able to mate with African jacksonii?