Distance Between the Reader and Characters
A main disadvantage to using the omniscient point of view is the distance it creates between the reader and the characters. This might sound counterintuitive since the omniscient narrator knows everything about the characters and the plot, but the result is the reader's lack of connection to the primary characters. The omniscient voice is impersonal because the narrator tells the story word for word, rather than allowing characters to naturally reveal their feelings and attitudes as the story unfolds.
The omniscient point of view often leads to head-hopping -- the negative result of quickly jumping from one character's viewpoint to another character's feelings or emotions within a short time. Head-hopping is especially problematic when a scene contains multiple characters and the narrator bounces back and forth between their points of view within the same paragraph or sentence. It's difficult to keep the pronouns straight and remember which "he" or "she" the narrator is referring to.
A shortcoming with the omniscient point of view is that authors don't always make it clear whose point of view they're using. This leads to confusion. The reader might assume that the expressed feelings and attitudes represent one character, only to find out several pages later that they had the wrong character in mind. If the author doesn't introduce all the characters at the beginning of the story, a new character's point of view can seem strange and unfamiliar. Some authors forget to use asterisks or line breaks to let readers know that they're changing the point of view.
Problems with Limited Omniscient
The limited omniscient point of view greatly reduces the author's -- and the narrator's -- ability to answer a wide range of questions and provide a vast amount of detail. Readers can only experience the story from the selected character's viewpoint and can only go where the chosen character goes. Stories that have complex plot lines typically require more than one character's point of view. A single character can't naturally know about and participate in all the important events.