Watch that Lean
A leaning tree is not necessarily a cause for concern. If a tree has been leaning for most or all of its life, it has likely put on wood in the right places to adapt to the lean. Trees may lean in response to surrounding trees, available light, simple genetics or other reasons.
If you notice things like a change in lean, soil heaving around the base of the tree or cracks in the stem the tree should be further evaluated. If you are concerned about any leaning tree, have an arborist perform an inspection.
Branches of Failure
Trees with a large number of branches originating from one location can be prone to failure. Such branches have weak connective tissue and branch angles that have difficulty supporting branch weight. When these branches do fail, they often lead to large wounds that the tree has difficulty closing.
Ideally, such a problem would be fixed when the tree is very young. Most deciduous trees should be pruned so that a single leader grows from the top of the tree, at least when young. It gets difficult to prune the tree correctly when it is larger, because the pruning cuts will be larger. Such cuts can be difficult for the tree to close and can lead to decay issues. The best solution is to plant trees not prone to such branching.
Surface Root Problems
Surface roots can lead to problems such as root desiccation, lawn mower damage and trip hazards. They are often a sign of water and soil issues in a property.
Matching a tree to the site is the best way to prevent this, but once it occurs it can be alleviated with the careful application of soil and mulch.