It would be useful if there was a screen capture tool within the application, that would ideally work like snip, so screenshots of issues or steps could be taken straight from Lean testing. It would also be useful to then be able to assign screen captures to created steps, so the developer can logically see where each screen shot fits in the process of replicating the bug

Some test cases might be specific to a section. The bug reported when executing the test case should be auto-assigned to the test-plan section.

Inspiration is coming from github issues repository and this same Damn bugs' userecho issues list.

Could be useful that each user could add one or more labels to each tickets, in order to group and categorize each one. Then clicking on each one, could become a way to apply custom filters.

In my opinion, default labels names could be ok, but should be important that users could create new ones (at least who with Account manager role)

Add a reset filter button,
in addition when clicking a link that add a filter, it is reseting all applied filters but this one
(Ie on the dashboard, if I click the "new" link it shows me all the new ones and only these ones

This seems so obvious maybe I missed it?

When inserting a url into a ticket, it does not make the link active.  You have to manually copy and paste this into a new tab.  It would be nice if you could just click on the inserted link and get to where you need to go.  

when open the "project section" drop down in the bug report the names of the section are showing without any order and it takes a lot of time to find what you looking for.
adding simple "sort by..." will make things much faster and simple :)