Boats go through the floor sometimes when spawned on the ground and a player rides it.
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Confirmed in 1.4.5.

Updated summary and affected version
There's a special instance of this in 1.5 pre - Every single time you place a boat on land and get in it sinks down one block into the ground.
My friend found a bug involving boats and the new fetcher of logging out with boat entity.
He sat in a boat logged out and when he logged back in he sank into the ground from client side, but from the server side it still fine as shown in the pics attached.

Is this still a concern in the current Minecraft version 1.6.4 / Launcher version 1.2.5 ? If so, please update the affected versions in order to best aid Mojang ensuring bugs are still valid in the latest releases/pre-releases.

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Also, I cannot confirm this.
I think this is a duplicate of MC-119. They are talking about 'Mobs sinking through solid blocks'. A boat is not a mob ... ? True, but a boat is an entity, and so is a mob.
Please attach a description along with your video, not everyone has the time to watch a video. Something like 'Boats go through the floor sometimes when spawned on the ground and a player rides it' would be sufficient.