TITLE: Diplomacy when reporting errors
QUESTION [31 upvotes]: I am a young researcher and sometimes I face an uncomfortable situation : I find an error in a research paper! Of course, most of the time, it is all just my misunderstanding but it happens that after checking tens of times, there is indeed an error and therefore I am not sure what I should do. 
"Am I the first one that notices this mistake or someone has already reported it? and then where?" "Hass this error been corrected in a later version? How can I know? ", "Should I send an email to the authors ? But still how could I be diplomatic enough not to bother them (and maybe the mistake is still mine, I am not an expert of the field)? " 
The situation gets worse when 
-The paper is already old.  Personally I would find annoying if someone asked me questions on a project finished years ago. And for very old papers the authors can just be retired already.
-It comes from a different field like physics or chemistry. Where they use a different language. How could I explain myself correctly and without creating a "diplomatic crisis"?
So I am here to ask advice to the experimented researchers how to deal with this awkward situation.

REPLY [29 votes]: Of course, reporting an error benefits the author, so I advise to write to him/her. A polite form is: Dear X, I am reading your interesting paper Y, and I have difficulty in understanding why A implies B on p. C. I will appreciate it very much if you explain this to me (help me to understand). 
I received such letters several times. In most cases I was able to explain.
In one case I published a correction. And of course I am thankful to all who wrote these letters.
When I was a student I wrote to one famous mathematician: Dear X. Let me bring to your attention that conjecture W which you state in your paper Y seems to be proved by Picard in 1880 in his paper Z. Do you think his proof is correct?