What are the chances of side effects from Mesotherapy?

I do not perform this procedure but I generally have seen patients who have had it done and are dissatisfied. This is not an fair evaluation and may be biased because I rarely see patients that are satisfied with the results.
The number one complaint is that it didn't achieve the anticipated results. Also commonly reported is nodules or irregularities or firm areas or skin discoloration.
It is most likely that these are related to the products injected, doses, volumes, concentrations, injection technique, and regional anatomy.

During Mesotherapy procedure, a small amount of Mesotherapy solution is injected in the superficial layers of the skin. Some of the risks associated with these injections are inflammation, bruising, swelling, pigmentations in treated areas, infections. Risks related to the  Mesotherapy solutions: allergic reaction to a therapeutic compound used in the solution.
There are a lot of different indications for the use of Mesotherapy, and not all doctors are well trained in this procedure. It is advisable to see a physician who has particular interest and expertise in Mesotherapy. 

Mesotherapy generally under delivers and does not last long. Very few surgeons do it, but mainly something for those who cannot perform surgery. It is good to read more about it, Nasim Huq

Mesotherapy been used in Europe and else where for quiet some time. I’m sure that some practitioners have achieved a level of mastery in using this technique without complications. The picture is a little different in the US. I have personally seen in my practice many patients treated else where that were not happy or had complications. It could be the provider fault and not the technique but I still think there are many problems related to this technique e.g. bumps, discoloration, fat necrosis, muscle pain, etc.Hope that helps

The long term side effects of mesotherapy are both unpredictable and incompletely studied. This is only one reason I have hesitated to adopt this procedure although I have studied it. I have seen too many patients with pitting, lumpiness, irregularities in skin and fat, discolorations, etc., and there are too many physicians performing this without knowing exactly what they are doing and how much to use and how to apply it. Be Cautious! It is technically very easy to do and if the results were well known and effective most physicians would have adopted it already. Mesotherapy has been around for many years in one form or another.