When should I ask questions about a paper? Short intro: I am a masters student, and doing my master thesis in physics.
Currently I am working on a numerical physics project, and for calculating a formula I want to use an algorithm proposed in a recent paper. Unfortunately I am not able to fully understand and reproduce the algorithm, either because I am lacking some information, and I am also not sure if my implementation is correct at all (I am working with a numerical approximation method, they wrote, that their error changed while calculating (and therefore they had to implement a intelligent error algorithm), but my error never changes.
I am currently the person with the biggest knowledge both in numerical computation and in solving the GNLSE at my chair, so my supervisor can't help me, either.
So, when should I write the responsible author a mail and ask him about the missing parts in the paper? I don't want to annoy him with stuff like "oh look, I forgot a bracket", or similar things which I never saw. Is there a line to draw? How do I check if my questions are "clever" enough to ask?
I think a good general rule of thumb, when you don't know the authors in question, is when you've convinced yourself you can understand some piece of the paper (or resolve an apparent contradiction) with your current resources.  Once this is the case, try to craft a simple, brief and direct email which addresses the primary issue(s). Then sleep on it before sending it, as often things will be more clear the next day.

In your particular case, it seems reasonable to ask about details of the algorithm, but I would not ask about your implementation.  However, they may be willing to share their code with you if it is non-proprietary and not a complete mess (like most of my code!), which you can then use to understand the details of their algorithm and check your implementation.  (Have you already checked their websites to see if they made the code available?)