Are all Wii WiiWare and Virtual Console games available on Wii U eShop?

Question

Does the Wii U eShop contain all the WiiWare and Virtual Console games from Wii Shop Channel?

Are there any such Wii games known to be specifically not compatible with the Wii U (e.g. with regard to System Transfer)?

Answer 1

No, it does not.

Nintendo currently only sells a small fraction of the Virtual Console titles on the Wii U as they are converted to Wii U for controller compatibility and other reasons.

You can still purchase these games on the Wii U from within the Wii virtual machine environment via the Shop Channel and Nintendo is still distributing games for the Wii through this shop (including some of it's Club Nintendo giveaways).

It is very unlikely that many if not most of these games will ever be ported for native Wii U play due to the radical change in controller schemes. All Wii U games are required to support the tablet as the primary controller.

As for the second part of your question, the only significant game I am aware of that will not transfer to the Wii U's Wii emulator is Lost Winds. I have also found anecdotal evidence that DLC for Final Fantasy The After Years fails to transfer as well and neither can be downloaded from the Wii Shop Channel on Wii U.

One added note as this was touched on in comments. Nintendo has indicated they will re-issue an unspecified number of Virtual Console games on Wii U and if you have already purchased the Wii version and it is linked to the Nintendo account you transferred from a Wii to the Wii U, then the new release will be offered to you at a greatly discounted prices ranging between $0.50 to $1.50 in the U.S. (if you did not transfer your Wii profile to your Wii U then you are not eligible for the discount).

Correction: In April 2014, Lost Winds became transferable from the Wii to the Wii U. To transfer it you will need to have held onto your old Wii system and repeat the transfer process. Otherwise you'll need to repurchase it.