A solidly-built, full scrub dozer canopy with risers, is a necessary addition to a crawler when you start knocking down trees. A tree spear is a useful addition for bigger trees.
Examine trees as you approach them, assess them for dry rot, termite damage, anything that can weaken them, and make them collapse onto your machine.
Watch out for forked limbs that fall onto the canopy, with one limb staying on top of the canopy, and the other swinging under the canopy roof, to smack you in the head!
Watch out for stray limbs poking into radiators, hoses, belly compartments - anywhere where they can cause damage. As terex herder says, tree limbs are out to get you, every minute of the day!
Watch out for a buildup of dry sticks and leaves and debris that builds up in the engine compartment - and especially around the exhaust manifold.
You can start a fire quite easily if you allow the sticks and leaves to build up. Clear them out daily. Carry a fire extinguisher, or at least some water, on the tractor.
It's easy to bend panels and guards and tinwork by not watching stray limbs and branches when you're pushing them.
Been there and done all that, I've cleared probably over 150,000 acres - including many thousands of acres of chaining, in my earlier dozing career.
Nowadays, clearing in my neck of the woods is limited, and very tightly controlled, the problems of overclearing took 30-40 years to show up.