A few days ago, I tackled this question from a reader: "What are some of the major things to avoid besides the dreaded Head Hopping?"
In my original post, I covered why don't believe head hopping is necessarily bad or something to be dreaded. However, there are definitely various problems an omniscient narrative writer must take care to avoid! Here are a few that spring immediately to mind.
1. Information-dumps. This is a problem that can occur in any narrative voice, truly. But the omniscient narrative does tend to provide writers with grander opportunities to fall into this trap since you can info-dump from SO MANY POINTS OF VIEW ALL AT ONCE. Or, as the narrator, run into long-winded descriptions and explanations of characters, settings, cultural practices, histories, or whatever, none of which directly relate to the plot or characters.
Good writing is tight writing. Don't get lost in information that doesn't matter.
2. Too many characters. Because the omniscient narrative is so flexible as far as point-of-view is concerned, it's easy to start bringing in new characters who don't actually contribute to the story you're trying to tell. And then to ramble off on rabbit trails about these characters because you've become attached.
Again, good writing is tight writing. Don't bring in characters who don't actively contribute to the story you are trying to tell. The reader only wants points-of-view that further the plot--they don't want your rabbit trails.
3. Summarizing. This one is a huge temptation to writers of the omniscient narrative. It's also not always something to be avoided . . . sometimes a good sum-up can really work! But in general, you want to spend your time telling the immediate story taking place, not rambling on in summary. Let's say the heroine's father died. Don't spend three or four paragraphs filling me in on what happened to her over the next three or four weeks--how she arranged the funeral, who brought meals to her house, how often she cried, etc. etc. Pick a specific scene sometime within those three weeks and show me her reactions to her father's death. In the context of that scene you can slip in some summarizing information, but keep the focus on the immediate scene itself. Give me character and give me story. Don't give me summaries.
This one is a problem for omniscient narrators because a good omniscient narrator can summarize things with clever and personable turns-of-phrase, etc. The narrator is herself a character in the story, so it's easy to let her dominate. But ultimately your writing will be stronger the more immediate-scene-focused you are.
Again, this one is not always a problem. Sometimes a summary can be just what you need. Sadly there's no hard and fast rule about when it works and when it doesn't work. This is where practice and finesse comes into play.
4. Too many story lines. The omniscient narrative is wonderful in its flexibility! It is by far the most efficient narrative for telling a complex plot with multiple plot threads. But, just as it's possible to try to handle too many characters at once, it's also possible to try too many plot lines. The narrative might be able to handle them, but the story might not. Keep it tight, keep it focused. Have clear goals in mind and a specific climax toward which to aim. Only allow in as many story lines as will serve your ultimate purpose.
Those are the only pitfalls to watch for that I can think of just now. Let me know if you can think of any others you'd like to share in the comments! And let me know if you have any follow-up questions as well. This is quite a broad topic, and I'm sure I could write many weeks' worth of blog posts without running out of new things to say.