So I get that špatny could be worng and bad. But how would you denote one over the other? The tree can be the wrong tree, but what if it's a bad tree for whatever tree related business i might have?
Without context, which we don't have here, you really can't. In this exercise, BAD, WRONG and INCORRECT are accepted.
Just add a little context basically. Or use a synonym—nesprávný is an example for incorrect or mizerný is an example for crummy/lousy as in the bad tree example you gave.
How do I know if an adjective whose stem ends with -n- is going to be hard (špatný, jiný...) or soft (poslední, zvlástní...)?
How do I get the right accents on my (nokia, android) phone?
Install a Czech keboard layout, there are many. Even the default keboard app should support it.