Birds' nest? Hornet's nest? Squirrel nest? Ist two unlikely to be occupied or active right now...the third unlikely to have babies yet if occupied (most aren't).
If it is a birds nest, do you know what type of bird it is? Some are protected and it can be a federal offense to disturb their nesting sites.
Do you mean other than the nest what things should you be worried about? If that is the question then I have a couple for you. How big is the tree? What kind of tree is it? How close is it to your house? Do you have a licensed contractor or one with liability insurance contracted to take it down? Have they discussed what they are going to do with the debris? Have they discussed what they will do with the roots? Have they discussed how they will handle the clean up?
it is a bird nest, in a sweet gum tree. about 20 to 30 feet from the house. I do not know what kind of bird occupied the nest, but I'm reasonably sure it was a common seasonal bird. no eagles or hawks.
If you do not see activity at the nest I don't think you should be concerned. Birds could nest in a tree that would come down from natural causes from one season to the next.
If it is made of leaves. it is probably a squirrel's nest otherwise it is a birds nest and won't be reused until spring if at all. Most bird's rebuild each spring. Take the tree down now.
I was thinking it was a squirrels nest too. In that case, we won't miss one less tree rat, though they are precious looking when they are babies.