The eat anything and everything.
They can be aggressive during breeding seasons.
Often preventing some from doing yard work or getting to their car etc.
Many homes have screened in lanais and pools that cost several thousand dollars only to be ripped apart by climbing igs.
Urates and poop that cover decks, boats, cars or any other surface.
Many cities require you to pay a "invasive species" tax for maintaining low numbers.
Giant holes and divots in yards during gravid season.
Thats all I can recall from my dads list when he found out years ago that I was taking in rescue iguanas. There are probably more concerns that BB can list :)
Oh pool maintenance, or being unable to swim in said pool.
I am more of a "live and let live "type of person but I do understand not everyone feels that way :/