A tree that loses a lot of the limbs throughout the year. In this situation where a tree is losing a lot of limbs could indicate a poor buffer area, too thick of limb count in the area of the tree, too long/heavily loaded with weighted branches. This could all cause poor health/conditions, stability of the tree.
Split tree trunk that could be from significant high winds, lightning strikes, double trunked trees coming from one stump which are also called “schoolmarm/cluster” trees. These trees are especially dangerous because they have poor growth from the stump due to the variations in the fiber of the wood. As these trees grow they grow apart from one another with heavily loaded branches causing significant stress at the stump.
Any visual decay or wrought would indicate poor health/declining of the tree. In some situation this decay or wrought could be caused from too close of excavation for structure dig outs, driveways, sidewalks, patios causing that area of the tree to decline. If the root is cut to close to the tree trunk that portion of the tree will in due time show visual decay and wrought. If the soils around the tree are saturated throughout the year that will promote a root wrought in certain trees as well leading to visual decay and visual fungi growing from the tree trunk.
If you see things like excessive woodpecker holes or small holes with small sawdust piles at the base of the tree would indicate excessive pest damage. These trees are dangerous because the structure is weakened due to pest eating the tree fibers leading to the wood peckers trying to get to the pests. Woodpeckers working on a tree usually indicate a declining tree.