I would like to see a different element other than <aside> to be used for content that is separate from the main content of the page and is commonly found on the side of a page. I know the definition of <aside> has been broadened to include being used for this purpose, however I believe this makes things more confusing.

A new separate element such as <mod> (module) would be more appropriate for miscellaneous blocks of secondary content on a page. This would be a more appropriate name than <sidebar> since it won't be confused with how that term is used in printed publications (which is what <aside> is to be used for). Also, <mod> could be used to contain groups of <mod> and <nav> elements.

<nav>
    <h1>Main Menu</h1>
</nav>
<mod>
    <h1>Current Weather</h1>
</mod>
<article>
    <h1>Article</h1>
    <p>Paragraph</p>
    <aside>Aside</aside>
    <p>Paragraph</p>
</article>
<mod>
    <h1>Search</h1>
</mod>
<mod>
    <h1>Advertisement</h1>
</mod>