I'd like to see my dates roll up the hierarchy so that I can see higher level estimates as they roll up. For example, if I have a folder for a project and I have a number of tasks underneath, I'd like to see the latest due date in the project, or the earliest start date.

As a gantt user, I would like to get my the release date of my versions automatically projected as milestones on the timeline, so that when I bind a task to it, it automatically update the fix version/s field.

To provide a backlog forecast it is essential to show what content could be done within a certain time or time budget. If we configure the budget in a top level issues custom field, structure could SUM not only by level, but also the contents of the current list of elements (eg. by priority) and a formula could show from which element the budget is overspent.

Our users will customize their view, setting the column widths in a way that allows them to best see the data in the view. While Structure does a great job of preserving this, in their session, there is no way to save the column widths, either in a saved view or in the "perspective view", from the Share button. Our users would like to share these adjusted column widths with other members of their team.

Automation + Grouping on Multi-Cascading Select fields is a top-notch function that allows users to efficiently organize complex datasets, but are functionally limited to deeper organizations.

If I start using the Jira-system 2-tiered multi-cascading select field in Structure for my issues, but then decide I need to switch to a 3-tiered mutli-cascading select to model my data, I sacrifice the functionality of Structure for the flexibility of another add-on.

Including support in Structure for n+ Multi-Cascading Selects, e.g iDalko's multi-select field (using MySQL), would help users like myself fully harness the capabilities of automated issue structures

I would suggest you to resort exclusively to the AUI objects for your interface instead of your custom ones that clearly gives the impression that you are exiting the Jira world to step into another one.
I think you user would deserve a smoother user experience, with the same kind of buttons, icons, tables to which they are already used to. I'm especially talking about the transformation/filters features that should be improved in that direction to my mind. Thanks for you great achievement!

Budgets are often not added as issues. Structure could add value by allowing some limited amount of named custom fields on structure-folders (like notes, but some more). They would bind to a structure and could be accessed from formula columns.

The Structure 4.5 documentation doesn't identify how to create a NEW Formula Column.
https://wiki.almworks.com/display/structure/Formula+Column

Step 1 should identify how to add a new field, not how to write the formula.

I assume a lot of people want to use structure for reporting as well. Most teams work with sprints and therefore it is essential to be able to select "sprints" as a filter for worklogs in structure views. A structure/or view could show worklogs for a certain sprint only and besides also for the involved team as well

when you report worklogs with structure, you want to use the worklog column and specify a time period.
If you add multiple columns, it is quite an effort to change the time period from eg. dates of jan to feb. (currentmonth is helpful, but somewhat too dynamic if you want to compare months)

To easily switch between months it is necessary to switch the time period you look on on the view level and influence alle worklog columns this way.

E.g. to calculate a percentual distribution over all rows of a structure, for the formula you need the 100% value which is typically shown on the root element.

Therefore it would make a lot of sense, to be able inside "formula column A" to use a columns B's value, but the root element value! This should be possible even if column B is a formula itself.
As we can already use variables like "Column B ..." in formulas it would be nice to add "Root Value of Column B ..." to the variable selection list

The Structure 4.5 documentation is lacking when describing how to create new views.

For example, if I take "Basic View" and copy it to my Structure, I would expect that I could edit it, but the View Details screen says

Access: Use - you can use this view but you cannot update it.

There is no "Save As" button as indicated by the documentation.

Require the user to confirm a deletion of an issue before it is removed from the structure. Right now there is a message that an issue has been deleted, but my users aren't noticing the message. Need to make them verify the deletion before it will occur.

I create some rather large Structure charts with multiple levels of nesting. Want to be able to highlight aspects of the chart (Rows, Cells, Columns) with color. This helps with focus (these items are critical), organization and overall visual appeal.

When an issue appears multiple times in a structure (e.g. epic link and issue link),the progress calculation should be configurable to prevent / allow double counting

Structure formulas are extremely useful. Now our users would like ways of using them in other places within Jira. This may be tough in some ways because they are specific to the structure they are part of, but even something simple like the ability to choose an menu option or call some API to commit formulas into an underlying custom field could be quite useful.

With Synchronizers it is possible to limit the issuetypes. Therefore it is possible to have multiple link synchronizers for different issuetypes.

Example:
one could defined a parent/child link between epics and features and use a is blocked link between features and bugs. with automators this scenario can not be implemented at the moment.

In structure folders created based on custom fields will show "no value"-folder in case issues haven't set the related custom field. It would be nice to get an option to define whether to show such "no value" folders or to show such issues without a folder under their parent.