A student (a native speaker of German) used the expression "without doubts" to start a sentence. That sounds wrong to me; I would prefer "without a doubt". But instead of just marking it as wrong, I did a quick bit of research.
I searched the NOW Corpus at the Brigham Young University site with linguistic corpora. The NOW Corpus contains 3.3. billion words of data from web-based newspapers and magazines from 2010 to the present. And by the present, they mean the present: it's updated with 4-5 million new words every day.
There were 27 hits for "without doubts" and 7752 hits for "without a doubt." So I can correct the student's usage in good conscience.
And that is how a usage point can be resolved: check actual usage using a linguistic corpus like the NOW Corpus (or any of the other corpora at the BYU site).