No, the passage "It’s accidentally spilled all over the desk." does not contain a sentence fragment error. It is a complete sentence that expresses an action being described.
Yes, the following passage contains a sentence fragment error. The phrase "It's accidentally spilled all over the desk." is a sentence fragment because it does not contain a subject or a main verb. It is missing the subject that is performing the action of accidentally spilling something. To correct the fragment, you could revise it as follows: "The water bottle accidentally spilled all over the desk."
