General Misunderstanding:
* Misinterpret: To understand something incorrectly.
* Misunderstand: To fail to understand something correctly.
* Misapprehend: To fail to grasp the true meaning of something.
* Misconstrue: To interpret something in a wrong or mistaken way.
More Specific Nuances:
* Distort: To twist or change the meaning of something.
* Confuse: To mix up or fail to distinguish between different things.
* Misjudge: To form a wrong opinion or assessment of something.
* Overlook: To fail to notice or consider something.
* Misread: To interpret something incorrectly, especially written or spoken words.
* Miscalculate: To make a mistake in calculating something.
* Misapply: To use something incorrectly or for the wrong purpose.
The best word to use will depend on the specific context of the situation. For example, if someone misunderstands a joke, you might say they "misinterpreted" it. But if someone fails to understand a complex scientific theory, you might say they "misapprehended" it.