Is it accepted/common to answer factually inaccurate reviewer comments in case of rejection? I recently got a paper rejected. I do not plan on appealing, I definitely see that some elements of the paper need improvements.

Nevertheless, some of the comments from one reviewer are factually inaccurate.
For example, I cite Paper A, where claim X is made. This reviewer says (repeatedly, in three different comments) that


  The author [me] claims X without proof and does not cite a reference


There are also other inaccuracies from the same reviewer.

Would it be appropriate to write to the editor to answer this kind of factually inaccurate statement?
I have not read your paper and it's likely that you don't work or publish in my field, so you will need to take this advice as it is given: without conditions or obligations.

I have decades of experience helping edit some of the top journals in my field. If I've learned anything, it's this: as much as academics like to think otherwise, peer-reviewed publications operate in much the same way as [insert trashy supermarket checkout rag here]. Journals are human institutions operated by humans with the same human concerns as everyone else. Things would go a lot smoother if they stopped being placed on pedestals.

Despite everyone's best efforts, mistakes happen all the time. From an editorial point of view, it is important to us to receive reports of factual errors so that we can consider the best information to reach the most appropriate decisions.

If you were to write to us about this issue, I promise you that we would consider this seriously. While we value the work our reviewers do, we also need to know when our reviewers are making factual errors such as this. This is actually a red flag for us. 


Why did the reviewer fail to pick up that these statements were referenced in the text? 
What else did the reviewer misinterpret? 
Is this behaviour consistent with other rejoinders or complaints we've received? 
Is it still worth our while keeping this person on our list of reviewers?


It is for this reason that I recommend that you compose and send a letter to the Journal making these corrections. It is unlikely that the issues you outline will overturn the decision and, by your own admission, you're not seeking an appeal. Nevertheless, I believe that this is an important step. There's no need to be uppity about this. Just lay out the issue and sign off.

In addition, you might want to reconsider the manuscript to see whether it could be improved to prevent this issue from being raised when you submit your work elsewhere. For example, you might have wrote


  We collected and analysed blood using standard techniques. Levels of serum bicarbonate...


when something like this might be more specific


  Analysis of serum bicarbonate was conducted using the process outlined by Nikishima et al. [5].


I'm making this up, but you get the idea. Could your statement be modified slightly so that there is absolutely no way for a reviewer to raise the original concern?

Anyway, good luck to you.