The problem is that I don't know if question means "doubt" or "problem". Question today is mostly used for "pregunta" in Spanish, but in Spanish we know this quote as:
Ser o no ser, esa es la cuestión.
I think it's mistranslated because "cuestión" doesn't really mean question, which is instead "pregunta". The beginning of the phrase is translated correctly though.
Puesto de otra manera:
La cuestión que estamos discutiendo es si debemos ser o si no debemos ser.
La pregunta que tenemos ante nosotros es, ¿ser o no ser?
Una pregunta es algo bastante directo, es decir, una oración interrogativa. Una cuestión es algo a problematizar, discurrir y discutir, que es lo que se hace después de este verso (que es el inicio de unos 30 versos de Hamlet).
To give some context to what is easily one of the most famous quotes in history:
"To be, or not to be" is the opening phrase of a soliloquy spoken by Prince Hamlet [...]
Although called a soliloquy, Hamlet is far from alone since Ophelia is pretending to read while she waits for Hamlet to notice her, and [...]
Even so, Hamlet seems to consider himself alone.
Source: Wikipedia
So Hamlet is asking a question to himself. We could change the sentence, maintaining all the meaning, by saying:
To be or not to be, that is the conundrum:
Whether 'tis Nobler in the mind to suffer [...]
since a conundrum is "a confusing and difficult problem or question; a question or problem having only a conjectural answer; a riddle".
And by doing that I hope it is clearer to understand the difference when translating to Spanish "question" as cuestión, instead of pregunta.
From the definition of "cuestión":
Pregunta que se hace con intención dialéctica para averiguar la verdad de algo.
Problema que debe ser resuelto.
Oposición de términos lógicos o de razones respecto a un mismo tema, que exigen detenido estudio para resolver con acierto.
We can see how the definition of cuestión explains the term as a "pregunta", but a pregunta that you make in order to learn something (like a rhetorical question in order to help someone understand something or to make them think, like in the Socratic method).
Thus, "question" has been correctly translated in this context, since Hamlet is not asking anything to anybody present in the room. He is more or less thinking aloud and philosophizing. He is talking about this philosophical problem, this conundrum.
You could have used pregunta in the translation, losing little meaning, but for Hamlet this is not actually "a question" (una pregunta / la pregunta) but "THE question" (LA [gran] pregunta). Thus, it is more a conundrum and philosophical riddle than a question per se (even a rhetorical question), and the translation favors the appropriate term cuestión over pregunta, duda, tema, etc.
