There is nothing terribly wrong with the sentence structure per se, but it has an effect that may or may not be desirable, and probably is not desirable quite as often as you are doing it: it changes the emphasis on the action being described.
Each of these sentences describes two actions, one leading to another:
Doing X he did Y.
Which of these two actions merits more attention from the reader? Normally the final action is the more important.
John walked into the bank and pulled out a gun.
But when you use the form in question (I don't know if it has a formal name either), you suggest that the first action is actually the one we should be paying the most attention to, or at least that it merits equal and continuing attention.
Slipping the ring from his pocket, John got down on one knee.
Notice how this sentence puts the emphasis on the ring rather than the knee, or at least that it keeps the attention on the ring while he gets down on one knee. Compare to:
John slipped the ring from his pocket and got down on one knee.
Using the conjunction makes these two separate actions and so we move our attention from the first to the second. But using the gerund form connects the two together, so that our attention is held on the first while the second takes place:
Slipping the ring from his pocket, John got down on one knee.
That is where we want the emphasis in this sentence. But contrast this with:
Walking into the bank, John pulled out a gun.
Walking into the bank is just how he got there. It is pulling out the gun that matters. Connecting the two actions like this distracts us from what is important, putting the walking in on par with pulling out the gun. In this case, it would be better to use:
John walked into the bank and pulled out a gun.
So ask yourself in each case if you want to connect the two events you are describing in this way. The answer will probably be that you only wish to do so occasionally. Where the connection is not desirable, use a conjunction or break the sentence into two.
