Ceiling Fan Mount Plate - You know what? The name of this article is just out-and-out misleading. The sole real "disadvantage" when it comes to a ceiling fan is what it requires to get one properly installed. Ceiling fans might be hard to install for the inexperienced do-it-yourselfer. In some instances, where the ceiling fan will be installed, you will need to run an electric line to the region. Hiring a capable, bonded and licensed electrician will more than likely save you much grief in the future, unless you're adept at doing this sort of thing.
There's also the minor "disadvantage" that entails the problem of periodic maintenance. Correctly installed, a ceiling fan will provide years and years of enjoyable cooling and cost-savings on your heat bill (assuming you have a fan that allows one to reverse the blade direction).
On occasion, ceiling fans get out of equilibrium and need minor adjustments. The most frequent offenders are loose screws that attach the blades to the motor housing, blades which aren't at the same angle (pitch) as the remaining blades and a blade or blades that weigh somewhat more than the others. Be sure that all the screws are tight, without going into great detail. Whenever they truly aren't tightening the ones that have come loose and run the fan. Your issue was solved, if the wobbling has ceased.
If not, make use of a yardstick or another straight piece of wood and put it (together with the fan stopped) vertically in the outer edge of one of the blades. Rotate the blades by hand to ensure that the stick is touched by each blade. If one or more don't, only (and gradually) bend the blade(s) so that their pitch matches the others and repeat the procedure until you're satisfied that each blade has the same pitch. Turn the fan on again and see if you've solved the issue.