Arguably the biggest mistake you can make is with "topping" your tree. It's considered something of a dirty word in horticulture circles. Topping means cutting a tree back so severely that only the stumps of large branches are left. It's done in an attempt to control the size of the tree. This stresses the tree because it takes away the leaves, its food sources. The tree will send out many smaller branches in an effort to produce more leaves quickly but they are not as strong as the previous branches and can break off easily in the wind. Tree topping also results in a pretty unattractive tree.
The way to properly bring a tree down in height is to make your cuts at a joint. A joint is the place where either a leaf or a branch grows out from the stem. Cut down the tallest branches at a joint, which will reduce the height significantly, instead of leaving a bunch of stubs. This way, the tree will be able to heal itself, growing a new branch in that spot.