The most accurate translation would be extraordinary as if you want to say strange, odd or weird you use rather word "divný" (derived from "divit se" (to wonder) which is relative to word "dívat se" (to look)) It can also mean particural, special, concrete especialy with conection to word "případ" which means case. Zvláštní případ means particural special case. Special theory of relativity could be rarely translated as "zvláštní teorie relativity" and it does not mean that the theory is strange. :)
The basic meaning of "špatný" is "bad." You can see some other translations here: https://glosbe.com/cs/en/%C5%A1patn%C3%BD. Since I'm learning, too, I can't tell you which are the most common ones, though I'd guess they're the ones near the top of the list. But in the course (so far...) it's usually appeared as "bad," "poor," and occasionally "wrong."