I apologize for the lack of punctuality in my response. I’ve been dealing with some health issues that have kept me from checking in on this.
4 combining diacritics that do not work (they also cause the character with which they are combining to be rendered in a different font as well):
◌́ (U+0301) [only when combining with another character that already has a diacritic like ā (U+0101)], ◌̄ (U+0304), ◌̮ (U+032E), ◌ͅ (U+0345)
10 normal characters render in a completely different font:
ḇ (U+1E07), ḏ (U+1E0F), ḡ (U+1E21), ḥ (U+1E25), ḫ (U+1E2B), ḵ (U+1E35), ṣ (U+1E63), ṭ (U+1E6D), ṯ (U+1E6F), ẓ (U+1E93)
11 superscript characters that seem to render in a different font, but I can’t tell as there are no other superscript letters to compare them to:
ˀ (U+02C0), ˁ (U+02C1), ᵃ (U+1D43), ʸ (U+02B8), ᵊ (U+1D4A), ᵒ (U+1D52), ʰ (U+02B0), ⁱ (U+2071), ᵉ (U+1D49), ʷ (U+02B7), ᵘ (U+1D58)
These are all used in the transcription of various Ancient Near Eastern languages. If there was an option to change the font in the program, it would be easy to fix on the user-end of things.