I've played the game twice so far today and encountered a couple of different CTD's.
On my first play through everything was working well. I was able to complete the default research, then the research on laser rifles, and then I was able to start constructing laser rifles. I managed to get two completed before I had my first UFO encounter. I successfully shot down the UFO but when I attempted to send the Skyranger to the UFO I did this by selecting "Launch Aircraft" on the Geoscape rather than clicking on the crash site and selecting "Begin Mission" from the Armoury screen. The steps I followed were as follows:
Select "Launch Aircraft"
Select the crashed UFO as the target
Select the Skyranger as the interceptor to use
Select "Launch Interceptors"
The game immediately CTDs and this seems to be consistently reproducible in a different save game.
Once I was able to launch the ground combat mission, I found that I could not save the game within the mission. It looks as though the save is happening, but no save game is created. I tried this multiple times but to no avail. No issues saving in the Geoscape, but I couldn't save when in Ground Combat.
Once in ground combat, I had a soldier that was injured by alien fire. I moved another soldier over and attempted to use the medkit to heal them. Instead of healing the soldier I seemed to end up stunning the soldier. Unfortunately I didn't take a screen shot, but while the initial text seemed to indicate a heal, at some point it changed to stun. I could have clicked twice, but in X1 if you healed twice the second time it didn't do anything.
My second CTD came at the end of the ground combat. I was able to successfully kill all the aliens but as soon as I killed the final alien on the probe I encountered a CTD - likely when I would have received the mission success screen. I've no save file due to the problems mentioned previously, but I've attached the output.log and recording file from that second CTD - couldn't find anything from the first one.
I'll keep testing but please let me know if you need any additional information.
output.log
recording_6.rec