It’s important to note that these red underlines don’t necessarily indicate a mistake, though. More accurately, they indicate that the word you typed doesn’t appear in Microsoft Word’s dictionary, and although it’s a fairly comprehensive dictionary, it certainly doesn’t contain every known word. As a result, all sorts of names and specialised words that you type correctly could be given the red-underline treatment.
A good habit to get into is to add those to Microsoft Word’s dictionary so that it recognises them in future. That way, you’ll notice any words that really were mistyped and – more helpfully – a finished document should always be pleasingly free of red underlines.
Adding words to the dictionary is easy: when Microsoft Word gives them a red underline, just right-click them and choose Add to Dictionary from the context menu. (Make sure you really have typed them correctly before doing this, though!) Straight away, Word will remove the underline from the word you right-clicked and, whenever you type it in future, it will be treated as correct.
You should take great care however as your Word Processor is unlikely to spot words which are actually spelled correctly but used in the wrong way. For instance if you meant to say "tongue" but you typed "tong" your WP will ignore it as it is in itself a correct word.
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