Of course, reporting an error benefits the author, so I advise to write to him/her. The 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 very much if you explain me (help to understand) this. 

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?