I believe one of the biggest improvements that can be made to Evernote without changing much of the product's base is to promote Saved Searches to a "first-class citizen" status, like Notebooks and Tags.
After a while, just tags and notebooks are not enough to organize everything, so I rely heavily on saved searches to use Evernote. But the functionality is very hidden and not very intuitive to use.
My suggestion would include some things like:
1. Place a "Saved Searches" icon on the sidebar, along with "Notes", "Notebooks" and "Tags" (same hiearchy)
2. Implement a screen