How sloppy is someone that they don't check their references!

A reference is included in a paper if the paper uses information derived from the reference, or to acknowledges the reference as a prior source. If the reference is fake, then the derived information could very well be fake.

Let's say that I use a formula, and give a reference to where the formula came from, but the reference doesn't exist. Would you trust the formula?

Let's say a computer program calls a subroutine with a certain name from a certain library, but the library doesn't exist.

A person doing good research doesn't need to check their references. Now, they could stand to check the references for typographic errors, but that's a stretch too. Almost every online service for retrieving articles includes a reference for each article that you can just copy and paste.