I am not able to reproduce the issue using the given information.
0023578 might be related.

I think this is exactly the issue. I didn't find this one.
When is the release of 2.9?

0023578 does not change any functionality, this is just a documentation change.
See documentation of $g_datetime_picker_format and the new warning for it http://mantisbt.org/docs/master/en-US/Admin_Guide/html-desktop/#admin.config.date

Oh I see.
in my config the dateformat is defined as the following:
$g_short_date_format = 'd.m.Y';
$g_normal_date_format = 'd.m.Y H:i';
$g_complete_date_format = 'd.m.Y H:i T';

This is common format in germany.

I've attached you some screenshots, you can see the original date and what the dialog/selector looks like.
After saving (the "unchanged date"), it becomes the current date.

a.png (3,273 bytes)   

a.png (3,273 bytes)   

b.png (2,236 bytes)   

b.png (2,236 bytes)   

c.png (16,058 bytes)   

c.png (16,058 bytes)   

I am not able to reproduce your issue, at least if I am following the documentation mentioned at 0023606:0058164 which tells you

This format needs to match the one defined in $g_normal_date_format

I don't see any problem when setting

$g_datetime_picker_format = 'DD-MM-YYYY HH:mm'; 

But the dateformat is
"d.m.Y H:i", as it is common in germany.

I've solved the problem by changing the format to "Y-m-d", which is easier for sorting.

I am not sure if you read the documentation, especially the note

The formatting convention for the DateTime picker is different from the one used for the other date settings described above

The picker date setting uses this format http://momentjs.com/docs/#/displaying/format/
whereas all other date settings use ISO8601 format https://en.wikipedia.org/wiki/ISO_8601

Can I set the issue to resolved, or do you think there is something wrong in Mantis?

I think it is still an issue, but since I was the only one, close it for now, I'm ok with it.

What's wrong when using the following settings?
Isn't this what you wanted before?

$g_short_date_format = 'd.m.Y';
$g_normal_date_format = 'd.m.Y H:i';
$g_complete_date_format = 'd.m.Y H:i T';
$g_datetime_picker_format = 'DD.MM.YYYY HH:mm';

if you use them, the datepicker doesn't work correctly, as shown in the picture.

I tried again using Firefox 57, Chrome 63 and Safari 11 and was not able to reproduce the issue.

Set to resolved as mentioned at 0023606:0058448