The bug

Be on the surface of water, look down, and right-click with a lily pad. The lily pad will be placed intersecting the player, which is not possible with normal solid blocks.

It is easiest to test this by standing in one-block-high water, but it works no matter the depth. Both Survival and Creative mode.

Also, if you stand on the edge of water (half on a solid block, half on water) and place a lily pad, then move out towards the lily pad, you will get the jumpy "stuck in midair" effect. Presumably this is due to client/server disagreement on whether you're on top of or falling through the lily pad.

As of 19w14a, placing a lily pad within yourself will also trigger the crawling animation.

Code analysis

Based on 1.11.2 decompiled using MCP 9.35 rc1

Placing lily pad on side of block

The class BlockLilyPad does not override the method net.minecraft.block.BlockBush.getCollisionBoundingBox(IBlockState, IBlockAccess, BlockPos) which returns no collision box.

Placing lilypad without looking at block

The method net.minecraft.item.ItemLilyPad.onItemRightClick(World, EntityPlayer, EnumHand) does not test at all if the block can be placed there or if entities (method World.mayPlace(Block, BlockPos, boolean, EnumFacing, Entity)).