The biggest issue I see is the writer not following guidelines provided by the contest or publication. Always check around for the guidelines. If they don't have any, follow Standard Manuscript Format. You can just look this up online. William Shunn has the best guide on SMF I've seen.
Here are some specifics I've seen done wrong:
You should use 12 point font in Times New Roman or Courier unless the guidelines ask you to do something different (which does occasionally happen). Everything in the document should be the same font. This means your title and byline should also be the same type/size as the rest of the document.
Use 1" margins all the way around, be sure it's left-justified, and only put one space after periods, not two. You can get to margins by going to "Page Layout" and selecting the "Margins" option.
To left-justify, look for the symbols at the top of your document that have a series of lines. Choose the one that has the lines lined up on the left, ragged on the right.
3. First Page
The first page is not just the first page of your manuscript - it should also convey certain information. Put a header on the top left of the first page with your name, address, email address, and phone number. On the top right, provide a rounded total word count for your submission. Include the title and your byline about half-way down the page, centered. Leave two spaces between the byline and the first sentence of your manuscript.
4. Indents & Spacing
Your submission is not an email or a blog post. This means the first sentence of each paragraph should be indented, there should be no extra spaces between paragraphs, and it should be double spaced throughout.
To indent, you can either use the tab button, or go to "Paragraph," "Indentation," and, under the "Special" pull down menu, select "First Line." Set it to .5".
To remove extra spaces between paragraphs (it should all look uniform if you've done it correctly), go to "Paragraph," and under "Spacing" check the box next to "Don't add space between paragraphs of the same style." You can also find the option for double spacing under "Spacing" then the "Line Spacing" pull down menu. Choose "Double."
5. Page Numbering
The page number should appear on the top right of each page except for the first page. The information on that page will make it obvious it's the first page. With the page number, you should have your last name and either the whole title of your work (if it's short) or an important word or two from it. To set the page numbers, go to the "Insert" tab and select "Page Numbers." Format from there.
To make sure it starts numbering on the second page, not the first, double-click on the header area of the document. "Header and Footer" tools will appear above your document. Click the box next to "Different First Page."
6. Page Breaks
To indicate a page break, don't put random symbols or lines there. Instead use a centered pound sign (#). This will let them know it's a page break, saving confusion.
These are just the things I see done incorrectly the most often in formatting. You'll want to look up Standard Manuscript Formatting to be sure you know everything you need to know about it. If there are guidelines listed for that contest or publication that differ from SMF, follow their guidelines for that particular submission. You'll need to adjust it to send to a different publication if it just wants SMF, though. To make this easier on myself, if a publication has different guidelines from SMF I will save it as a new document and apply the different formatting. This way, I don't forget that this document was different from SMF and send it formatted incorrectly to the next publication.
Good luck with your contest entries and submissions! Remember, always check their guidelines first, then go from there.
What are your critique or writing nitpicks? Is there something you want to see covered about submissions? What common mistakes did I miss? Any tips of your own?
May you find your Muse.