Minecarts fail to display specific blocks which you can specify in DisplayState.

One of the blocks they don't display are skulls.
Test this with:

summon minecart ~ ~ ~ {CustomDisplayTile:1b,DisplayState:{Name:"minecraft:skeleton_skull"}}

and this summons a Minecart with all the correct data as you would expect.
However the skull isn't rendering at all.

This is also the case for e.g. banners.
Summon command:

summon minecart ~ ~ ~ {CustomDisplayTile:1b,DisplayState:{Name:"minecraft:blue_banner"}}

List thus far of affected blocks which are not displayed (haven't checked all of them yet):

• Skulls
• Signs
• Banners
• Liquids (Water, Lava)
• End Gateway
• End Portal Note: It does display the Nether Portal Block though, but Nether Portal Blocks are rendered differently
• Book on enchanting table

It could be that this is due to skulls, signs, banners, end gateway and the book on enchantment table are block entities which are rendered via block entity renderer, but then again there are special cases such as e.g. chest, trapped chest, enderchest, shulker box which are displayed normally.

A more complete list of affected blocks - if there are any more than those mentioned - will be added over time.