Is there a way to see all the cards that have been assigned to a user on:
- a single board?
- across all the boards?
This would be much like the cards link below my profile box that I can click to see all my cards.
If you go to a member's profile (such as https://trello.com/aarond), you will see a "Cards" link just like on your own profile. This will show all cards that the person is assigned to on any board that you are allowed to see.
On a single board, you can open the right sidebar, open the "Menu", and click "Filter Cards" (or press 'f' on your keyboard). From there, you can filter the cards on the board by user (or by card title, labels, or due date).