Splatsch: Soooo... I spent some hours trying different things on my game, and I better understood some things and found some solutions (thanks to luck XD) that seems to work (it doesn't solve all, only the two of the issues that I have and that I'll describe now :) ).
1) When you want to disclose your first country and push the "disclose" button in single player mode -> World War : you have the left menu which have time to "begin" to appear (sometimes without units inside) and it always crash. Same thing in Hot-seat mode.
This issue seems to disappear when you install the latest available patch (the v.2.0.164 stated on my previous messages,
here or included into the package prepared by Lord_Kane on first post of this thread).
2) (First) Training Mission -> Movement and Combat -- The tutorial tells you to select your Heavy Bot. You select it (sometimes it crash here), and then, tutorial tells you where you must send it : when you want to move it and click where it must go (or even somewhere else for what I saw), it always crash.
This issue seems to be solved with remplacing some files in the folder "data\script" by some files from a fonctionning version of the game (retail). Here is the list of files who seems concerned :
antiair_alien_scripts.lua
helicopter_alien_scripts.lua
logic_utility_functions.lua
ltransport_alien_scripts.lua
ltransport_scripts.lua
mortar_scripts.lua
platform_scripts.lua
stransport_alien_scripts.lua
stransport_scripts.lua
If someone need it, I'll do a small package (because it seems that I'm the only one having this crashes).
On aside note, the training missions seems particularly full of troubles. I tested the Training mission 2, and information text goes sometimes too fast, like if you were constantly clicking to make it disappear (if it's what you were experiencing Lord_Kane). This seems to be solved with the Lord_Kane's fix in first post (thank you for your work).
So game is playable for me now (yay !) but I'll wait for GOG to provide a clean and proper version, seeing all bugs/troubles we encounter.
(I'll send them this complement, may be it'll help themto solve all of this).
DeadPoolX: I have a pretty serious problem too. When I load the hotseat game I was playing before, EVERY SINGLE UNIT turns invisible and can't be selected or moved. Even the cities are invisible and can't be selected as well.
Splatsch: I tried to reproduce your issue with a quick test (launched game, disclosed some countries, bought some units, moved them, attacked some untis... ) but everything was ok for me. Have you tried a new hotseat game ? But may be is this linked to Gamersgate version if it's the one you use, I don't know how different the versions may be (or even if they are different).
I am prepping a update right now to my fix pack which includes the scripts from my CD install and a couple experimental fixes.
EDIT: I put it up on the first post.