This is C we're talking about. Always be checking return values. (And errno! And errno! And errno!)
That said there are some functions where the possible return values can't indicate an error. In those cases errno should be set to zero before the function call and then a change during will alert you to an error.
Why it's like this I have no idea but it's pretty annoying.
The bit about errno possibly being non-zero but not indicating error unless the function does? I guess because the called function can itself call functions / libs which set errno and properly handle those (or just not care). Without the "errno only has meaning if the function returns error" guard, every single function needs to always reset errno to zero before returning, which is annoying and will almost certainly not happen in the majority of cases.
When the function has no way to communicate error, there is no other option but to use errno. But it's good that it's the exception, I imagine.
Can it makes things worse? Yes. But C is broken.
This is spot on. There are very few cases when silently truncating a copy of a string is an OK thing to do.