If you read an article saying that the area where you live will experience a major earthquake in the next six months, it is important that you know whether or not to believe the information. As you can see, the key to credibility is the question of trust. The author or source of the information should show some evidence of being knowledgeable about the subject at hand, reliable and truthful. Consider, for example, the author's background, training, and organizational affiliation. Statements issued in the name of an organization have almost always been seen and approved by several people.
Most educated people use grammar fairly well and check their work for spelling errors.
An occasional split infinitive or comma in the wrong place is not unusual, but more than two or three spelling or grammar errors is cause for caution, at least. For example, even though a very credible writer said something that was correct 20 years ago, it may not be correct today. In other words, the information should be comprehensive. No one can read 20,000 articles on the same subject before coming to a conclusion or making a decision. On the other hand, an information source that deliberately leaves out important facts, qualifications, consequences or alternatives may be misleading or even intentially deceptive.