On pc Debian x86-64 with master sources updated today, I could reproduce this.
I created a brand new doc, added some headings then created  a TOC.
Editing "Fill Character" in paragraph style doesn't change anything.

Interesting observation.. :)
To set the fill character for tabs in the TOC, one goes to 
 (right click) Edit Index or Table,
 tab Entries
 select the "T" in the line Structure
 and below you can change it.
There you can also set the tab indent. (Un check right aligned and enter a value).

AFAIR, it's always been like this.
I agree it is confusing.
On the other hand, in ODF there is the rule that indents of lists prevail over those set in paragraph styles. So in that light, this behaviour can be considered consequent.

Set as NotABug / WorksForMe ?

(In reply to Cor Nouws from comment #2)

Ah! That's good to know that there's an alternative that works.

Still, the fact that there's a work-around present in the program doesn't render the reported issue not-a-bug. Edit Paragraph Style is a function users are familiar with from elsewhere in the program, and when it comes up as an option, they'll be expecting it to work normally.

The Edit Paragraph Style window should receive the context of the click and, if an index or table was right-clicked, make changes as if it were the Edit Index/Table. Alternatively, if everything the Edit Paragraph Style window can do is duplicative of functionality in the Edit Index/Table window, Edit Paragraph Style should not appear as a right-click menu option to begin with.

Consider the case when page margins change. There is no way, using only the paragraph properties to mimic the "align right" checkbox to keep numbers aligned all the way to the right of the text paragraph area. If we were to use only the "Tabs" tab for the Contents N style, then, reducing the page right margin would leave numbers not really aligned to the rightmost area.

If you allow a suggestion: if I were a dev, this is what I would do:

1. Allow for a "%" unit in the [tabs] tab for the Position value. This would mean "percentage of the paragraph text area". "Align right" would be stated as Position: 100% with Type: right. This has uses beyond ToC.

2. Modify "Fill character" and "Tab stop position" so they are just another interface to the Nth tab defined in the "Tabs" tab for the "Contents X" style. So changing either will do the appropriate thing and reflect the changes accordingly on the other dialog.

Of course this has further implications, like file format, import and export filters, etc.

Step number 2 provided by the OP says "Insert a new Entry to the Table of Contents".

Is this referring to hitting ENTER to modify the TOC or to adding a header and then updating the TOC?

From my understanding of the reading it's the former, but LibO no longer allows modifications (contents or formatting) to the TOC once it's created. I think this is a good approach.

With the above, the way to change formatting for the TOC is through the style that correspond to the paragraph on the TOC. By default, this is Contents Heading and Contents 1 to Contents 10. Adjusting these styles will give a consistent look to the TOC, whatever it is. For example, adding some space before first-level entries (through the style Contents 1) will give it a consistent look than just changing it to one paragraph, or doing it individually.

I suggest to have this closed as being no longer valid.

(In reply to Octavio Alvarez from comment #6)

> I suggest to have this closed as being no longer valid.

also reading comment #2