You need to apply a character style in Word to the items with super- and subscript, italic, bold, bold italic, et al style changes in a paragraph of text, even in a single line paragraph.
When Importing to InDesign you can choose to "Show Options" of the word file and you can map the styles to InDesign styles for ease of transfer.
Alternatively, if the style names are identical then you can copy and paste the file into InDesign and the styles should be preserved.
The other thing to do if copying and pasting to InDesign is to go to Preferences>File Handling and choose to preserve text formating on paste.
Use a script
Alternatively there is a script to run on imported text from Word to InDesign which will apply a style to the text before editing can begin - http://indesignsecrets.com/perfectpreptext-a-smart-way-to-style-local-formatting.php
"You need to apply a character style in Word to the items with super- and subscript, italic, bold, bold italic, et al style changes in a paragraph of text, even in a single line paragraph."
Yep. That's what I did. Why then does it fail in InDesign? Are you saying that InD must be tweaked to accept these character styles, and it is not automatic?
I'm saying there's a preference in Edit>Preferences that it will take in plain text by itself or keep the styles
By default this setting is turned off and only applies to Copied Text from another document.
(My Appologies - the setting is in Clipboard Handling, not in File Handling)
And yes InDesign is not a Word Processing tool - it's a Page Layout tool - so it has options built in whether you want to include certain things with text, like the preservation of Styles and/or mapping styles around InDesign.
Could be the Font
Ensure you have a version of the font will all the alternates, like bold, italic, bold italic, and other formats required.
it may fail is because Word is a Word Processing application and it has an ability to Faux- Bold, Italic, Super, Sub et al things - this means that the Word Processor is applying a tweak to the text to get the appearance you are after and it's not inheritently built into the font.
InDesign does not do Faux Bold, Italic or other formatting - it uses the Fonts in-built definitions in the Glyphs to show the appearance.
If the font you are using does not have these alternates then it won't be able to display them.
It's most likely the Word Import settings that were last saved were set to import unformatted text, and you should have a conversation with the folks running ID....