Gmail's search lacks many useful features that are available in Google Web Search: the popular "did you mean" query suggestions, using synonyms to expand the query, searching inside PDF files or other documents, sorting the results by relevance.
It's one of the few areas that didn't evolve since Gmail's launch and I think it's embarrassing to place the "search mail" and "search the Web" buttons next to the same search box.
As you probably noticed, the web search button is now back in Gmail after a brief disappearance. A small number of vocal users complained and Google restored the button.
Here's how Gmail describes its search feature:
"You can use Gmail search the same way you'd use Google Search, by entering a word (or multiple words) that appears anywhere within the message you want to locate. If you're looking for a message that contains the word shopping, simply type shopping in the search field and press Search Mail. Your results will be displayed with your search terms highlighted in yellow. Gmail doesn't recognize special search characters like square brackets, parentheses, currency symbols, the ampersand, the pound sign, and asterisks. It also doesn't recognize partial or similar matches, so a search for travel will find travel, but not travels, traveler, or travle."
How would you improve Gmail search?