I mainly want to suggest that, if possible, we should be able to search with multiple tags. This could really help if somebody is trying to find a question by narrowing down the list of things with two or more tags. I'm pretty sure that this isn't possible now, but correct me if I'm wrong.
I would also like to suggest being able to search for only questions, answers, or comments when using the search function. Right now, if you search something, let's say "sauce", then the results that you'll get will include questions, comments, and answers with the word "sauce" in it. This can be annoying, because it adds a lot more results that need to be looked through. If we could had the option to search for just one of those, (Or maybe a combination between two of them) it could make finding things a whole lot easier.
Finally, I would like to suggest being able to search a user's questions and answers on the pages for a user's questions and answers.