Overly elaborate diction is what most think of when they hear the term "overwriting." I'd argue it's just one facet of a tendency to go thick, lush and heavy-handed when drafting. The trick is to identify and correct it during revision.
Your characters' word choices show us who they are, so it's important to be accurate. Generally word choices should be consistent with a character's age, level of education and socio-economic status. Just as a fifth grader wouldn't discuss post-feminist hegemony, a college professor wouldn't call his enemy "stinkypants."
There are exceptions, however. You might sprinkle in words like "indubitably" and "elementary" to show that your fifth grader fancies himself an amateur sleuth like Sherlock Holmes. A social climber might adopt fancy lingo but misuse it. A grade-skipping child prodigy would wield her vocabulary like a weapon.
As you revise, be willing to question your word choices. Advanced vocabulary can communicate some things you don't intend. It gives the impression that you, the writer, are insecure or a bit out of touch. It can also taint your characters with a popular stereotype: the evil genius whose intelligence is paired with heartless ambition, or the socially awkward hopeless nerd whose head is stuffed with useless knowledge.
As I wrote in this post, sound devices can be an effective tool to make your work sing. But if you're too heavy-handed, it sounds silly or just plain annoying. Generally assonance (repeated internal vowel sounds) is less jarring than alliteration (repeated initial consonant sounds) or rhyming, so you can be a little freer with it.
How heavy is too heavy? I don't have a hard and fast rule. If sound is a big piece of your style, you'll have a hard time identifying overkill. Ask four or five trustworthy readers who get your intent to help you trim all but the best of your devices.
Metaphor and simile can quickly become overdone. Beware of the tendency to describe every detail through comparisons. Watch out especially for inept comparisons that don't fit the character or situation. Stephanie at Hatsheput posted some hilarious examples of simile gone awry.
A whole-work "controlling metaphor" or motif is often fine, however. If done well, it can unify and strengthen your work. Sarah Dessen's Lock and Key, for example, uses the motif of doors, keys, fences, houses to examine what makes a place home, and people around us family.
Allusion can be an effective way to say a lot in a small space--your reader will pour in all the context without your needing to explain. But if the book, film, song or historical event you reference is too obscure, it hinders rather than helps your reader. A character whose thoughts are filled with allusions to pop culture will come across as shallow and lacking original ideas of his own.
Name dropping brands is another type of allusion that becomes irksome quickly. Call your fleece jacket a "North Face" once, then stick with generic terms like fleece or jacket in subsequent reference.
Take extra care when presenting a character whose regional accent isn't mainstream. The best way to handle dialect is through word order, cadence, grammar and word choice. But go lightly, especially with regionalisms like "youse guys" or "blimey" or "y'all." And as much as possible, stick to standard spellings. If you've done your research and can imitate the cadence and use the right lingo, your readers will "hear" the dialect without the tortured spellings.
Which of these diction areas trips you up? Any other helpful hints to add?