This morning when I opened my email I was very excited to find a Google Scholar update telling me of two new citations from two different sets of authors each to a different paper of mine. As usual, I immediately checked the papers to find out if the authors were praising or criticising my work (or perhaps they found a mistake in one of my papers!). To my surprise, in one case the authors wrote a misleading statement which resulted from stretching quite a lot some of my conclusions. In the other case, the authors simply made an incorrect claim (details below for the curious). It's not the first time this happens to me - I even got one citation completely out of context once. How to react to this kind of situation?
Details for the curious:
In the first case, the authors cite a paper of mine where I compare two different methods to calculate elastic properties of materials. My main conclusion is that one of the methods converges much faster than the other one with the size of the basis set - in other words, it's computationally much cheaper. For calculations with usual basis sets the first method is much more accurate than the second one, with disagreements between the two in the order of 10% or even 20%. They claim that I show that both methods agree within a 1% of each other, which is misleading at best, because for the second method to agree within 1% of the first one one needs to do a very expensive calculation. That is one of the main points of the paper and it got completely overlooked by the authors.
In the second case, the citation is plainly wrong. The authors cite my paper as an experimental work on InGaN semiconductors while it actually is purely computational.
You can draw conclusions about the quality of their work. Probably, it might be not a very high honor to be cited by them. I would most likely ask them to remove the technically incorrect references to my work, and supply the reasons for that.
They claim that I show that both methods agree within a 1% of each other, which is misleading at best, because for the second method to agree within 1% of the first one one needs to do a very expensive calculation.
There is a risk that the literature is now misleading. You could reduce this risk with a clarification, perhaps in a technical report version of your work. A diligent third party can now establish the truth.
For your second case:
the citation is plainly wrong
You can probably ignore this, since it is a clear error, which should not mislead.
Unfortunately, misrepresentation happens all the time. One tends to look for ways to prove they are right and someone else is wrong. It is then left to the audience to decide whether or not they want to believe their interpretation of the work. If one is made aware of the misleading or incorrect information, and one can, one should stand behind it. Sometimes the facts are misinterpreted because they were not delivered clearly and decisively. Therefore it may be helpful to include more information to clarify the work. The purpose of receiving the google scholar alerts of citations in the first place is to guarantee that one's work represents correctly. So as long as one can, and it matters, one should do their best to maintain the integrity of their work and the interpretation by others.