Another good deterent is automated lights and spraying natural preditor scents will help if the problem persists. Raccoons, possums and large field rats were a problem here when large amounts of construction were under way here destroying what was left of their homes. I dont know about your iguana but the damage you described is exactly what the raccoons where doing to my plants 2 years ago

I must agree with HDD,that its the racoons doing the damage.I have the same problem in the summer when plants are outside. The racoons are not after the leaves,but instead the beatles,slugs,worms,and other insects that take cover at night inbetween the leaves. This usually means they get down inside as far as they can toward the cup,and the racoons have figured this out.Smart buggers,and really annoying to all gardeners.There is racoon and deer repellent available in nurseries,don't know if it works,but my Mom always used coffee grounds in her vegetable garden for pest control and fertilizer.
Most plants affected by racoons for me this past summer were Vrieseas,and Neos,as they have the best leaf protection for bugs. Spiney ones,like some Aechmeas and Dyckia / Hechtia types were not bothered,tho sometimes up-rooted.
To add to our garden woes,racoons have big appetites,and in the Spring,have up to 6 offspring to feed as well.I've found that having automatic outdoor lighting that turns on by motion,does'nt bother them at all,and if anything,helps them to see better.;^(
Bob

get a coyote spray or any other natural preditor spray that will run the buggers off

Bromeliads have just become a new obsession for me within the last 6 months or so. Hey, you can only grow so many ridiculously large plants before you have to set your sights on something smaller!!! Anyway, this is the first spring for me with most of mine and I wasn't expecting animal destruction on them.

As long as the coffee grinds work, I'm happy. I like to peacefully co-exist with the wildlife my yard attracts, although I sometimes have to admit they can test your limits.

Last year, I used a "last resort" weapon from my arsenal--human urine. I saved throughout the day and applied at dusk around the perimeter, beginning in Spring. Frequent applications until early June established this as MY territory. My hostile acts quickly ended the frequent tipping over of bromeliad and orchid plants. I intend to reinforce my territorial claim starting next week. It's an organic repellent that kills nothing and is absolutely FREE! Don't yech...it works!

--Stitz--