Pretty much everything.
I've been using Steam version of the game to do the tests and it seems to run pretty well in you happen to install and run it under clean Wine prefix. Messing with some wined3d-related registry entries like changing "AlwaysOffscreen" to "enabled" or forcing game into using builtin d3dx9_*.dll could render the game into unplayable state but it's just the usual "shoot yourself in the foot" problem.
Game requires native d3dx9_36.dll (actually d3dx9_39.dll but Wine's builtin implementation of this lib forwards almost all calls to d3dx9_36.dll so one could easily use native version of any among these) to run. For Steam version of the game this library gets auto-installed as the part of DirectX redist installation - Steam client would proceed with automated install on the first attempt to run the game inside the given Wine prefix.
What does not
There's a minor bug with one having to press both shift keys to move a puzzle piece. This bug is not essential as (a) it's easier to use mouse for solving puzzles and (b) it's not a big deal to hold one shift key and briefly press and release another one to pick a puzzle piece.
What was not tested
Everything was tested, I had played the whole game through - it's not that long really.
Giving it "Platinum" rating as Steam auto-install required native DLLs so it is "works perfectly out of the box" situation from the users perspective. System specs: AMD FX 8120 CPU @3.1GHz, 8GB DDR3 RAM, GeForce GTX 550 Ti GPU with 1GB VRAM, nVIDIA Binary Driver v.275.09.07, linux kernel 18.104.22.168-3.lx2.fclx2.i686.PAE (it is kernel 3.1.10 which had been rebranded by Fedora devs to version 22.214.171.124).
|Operating system||Test date||Wine version||Installs?||Runs?||Used|
|Show||Linux Mint Debian x86_64||Aug 09 2013||1.4.1||Yes||Yes||Platinum||Alexey Loukianov|
|Current||Fedora 14||May 27 2012||1.5.5||Yes||Yes||Platinum||Alexey Loukianov|
|Show||Ubuntu 11.04 "Natty" amd64 (+ variants like Kubuntu)||May 09 2011||1.3.19||Yes||Yes||Gold||Vanack Sabbadium|
|Show||FreeBSD 8.1||Mar 22 2011||1.3.15||Yes||Yes||Platinum||Igor S.|
|Show||Ubuntu 10.10 "Maverick" amd64 (+ variants like Kubuntu)||Nov 09 2010||1.2.1||Yes||Yes||Platinum||an anonymous user|