In vector, the h1 and h2 use serif fonts (everything else is sans-serif). Unfortunately the font stack used results in a highly inconsistent user experience across different browsers, due to also affecting the visibility and or relative sizes of the headers.
The stack is thus: @content-heading-font-family: "Linux Libertine", Georgia, Times, serif;
Linux Libertine: Ideal font according to the current design. Relatively small, heavy serif font. Installed by default on pretty much no platforms.
Georgia: Relatively large, light serif font, when compared to Linux Libertine. Incompatible with some languages, also results in legibility issues due to strange rules for some character combinations. Installed by default on windows and mac(?).
Times: Somewhat generic fallback. Tries to go for a 'times' style serif or something. No different effect than 'serif' on most platforms.
serif: Generic fallback. Results in any number of different fonts, from DejaVu serif (which is downright ugly especially at larger sizes) to Times New Roman (which is smaller and lighter than Georgia).
Headers need to stand out in order to be effective, and the relative small sizes and lightness of some of these, especially when combined with relatively large sans-serif fonts in other headers/content text, limits this effectiveness on some platforms.
If the font delivered could be standardised (probably to the default, Linux Libertine), this could help to address many of the inconsistency issues. However, if core support for webfonts is not yet sufficient to handle this, is this font stack really appropriate at present given its inherent instability?
T65844: h3 should not be more prominent than h2 headings
T71998: Vector: h3 should not appear as heavier weight than h2
T71999: MonoBook: h3 should not appear as heavier weight than h2
T72004: h4, h5, and h6 headers should not have the same styling
T73240: Re-evaluate serif font stack for headers