I'm using LibreOffice Version: 5.0.0.1;
Build ID: 9a0b23dd0ab9652e0965484934309f2d49a7758e; Locale: en-US (en_US.UTF-8)
running on 64 bit Ubuntu 14.04 LTS.

When selecting the "Insert Special Character" menu item, the dialog correctly shows the name of the font in the Font: box, and the "Subset" choice seems to match the availability of scripts in whatever font is chosen, but the characters that are displayed are all from the same font (I believe it is my system font) regardless of whatever font is selected, and regardless of the script or font, the characters are all incorrect.

Thus, if I choose a character from some other script, the result is that an upper ASCII (Latin) character is both displayed and entered into the document.
At first I suspected I might have downloaded a 32 bit version by mistake, but I confirmed that I used LibreOffice_5.0.0.1_Linux_x86-64_deb.tar.gz and that this resulted in a LibreOffice_5.0.0.1_Linux_x86-64_deb directory.

This may be specific to Ubuntu, as another 'quirk' I noticed was that if I use the Ctrl+Shift+u command to confirm that direct entry of Unicode characters was still possible, the underlined u that usually appears doesn't. This still works, so the characters can be entered - the user feedback (the underlined 'u' is sort of a prompt) provided by the OS is hidden by the new release of LibreOffice.

Luckily I still had LibreOfficeDev 4.4 installed which I used to confirm that - as least as far as this "Insert Special Character" behavior is concerned - still works just fine. So while the bug (?) may be related to Ubuntu, I've never encountered it in previous versions of Writer.

Luckily some new default icons (Breeze) have been introduced to make up for the loss of the ability to insert "special characters." Even so, "Properties" and "Design" inexplicably use the same icon, so I returned to the Tango set.

Sigh ...