"That road is dangerous."
Is leaving です off sentences just informal or is it gramatically incorrect?
In most cases, it's just informal. However, there is an informal version of です, called だ, which is technically necessary for sentences ending with nouns or adjectival nouns (な-adjectives). Women generally will drop both in casual speech, but men generally use だ (since not doing so sounds girly).
い-adjectives are grammatically correct to end with. But it’s informal. な- adjectives are not grammatically correct to end with. You need だ or です.
“その道は危ない。” Is correct.
Thanks for the clarification, and my apologies for not being thorough with my earlier comment.
Ending a sentence with an い-adjective is informal but grammatically acceptable. Adding です makes it more polites, but adding だ is ungrammatical.
Ending a sentence with a な-adjective is grammatically unacceptable, but commonly done by women in informal situations. Adding だ makes it grammatically correct, and adding です makes it more polite.
Side note: these considerations happen before adding emphasis particles such as よ or ね, so 危ないよ and 危険 (きけん) ですよ are both grammatically correct, while 危険よ isn't (though it is commonly acceptable for women).
この (kono) - this near me
その (sono) - that near you
あの (ano) - that over there which is not near either of us
If you see "that" in English, あの or その should be okay, and if both aren't accepted it's worth an error report.