I tried it three times. The crash occurs after deployment but right before the battle starts.
errors.txt:
27/8/2010 - 5::59 - Assertion failure:filename:…\src\SIM_Battle.cpp,linenum:151,build:Full 1.46
27/8/2010 - 6::0 - Assertion failure:filename:…\src\SIM_Battle.cpp,linenum:151,build:Full 1.46
27/8/2010 - 6::2 - Assertion failure:filename:…\src\SIM_Battle.cpp,linenum:151,build:Full 1.46
Yep - but notice when you go to deploy - there is no visible enemy? For me thats a clue that something is not right. If I can’t see the enemy deployment I just skip it.
Berny
There are many crash-inducing challenges.
please list any others, I’ll investigate and remove them. This challenge indeed seemed unusable and has been deleted from the server. Unfortunately, I suspect it will still show in the lists of anyone who already downloaded it 
4612369
4601025
4591975
4600172
4601090
4601093
4601094
4603048
4609011
I wanted to investigate these a bit to see what might be causing the problem, so I tried to unpack them with the script snowdrift posted here: viewtopic.php?f=23&t=2828 but unfortunately that didn’t work… perhaps the .gsb file format changed in the past year?
The problem deployments are fairly easy to find, you might be able to automate it server side. I just look for challenges with no ratings (because the game crashes before you have a chance to fight, much less rate) and with attempts but no victories. A good proportion of these seem to be the game-crashers.
Then there is one more I found, 4609113, which crashes the game immediately upon download; the other ones above allow you to get to the deployment screen, but not this one. Hmph.
I will investigate when I’m not swamped with relatives, but I strongly suspect they are all challenges that have been accidentally posted as custom challenges, with no ships in. This was a bug (in that normally you can’t do that) which is fixed in the next patch.
At some point I’ll finish up code that will scan all the challenges for that sort of thing and remove any duff ones. It will also then (at last) correctly set the flags for every challenge in terms of which expansion pack content is used.
That does seem to be the pattern, as the preview pictures on all of these are devoid of ships.
Go enjoy your visitors! 
I’m investigating now…
edit: a whole bunch of invalid challenges are gone. I’m not sure tbh if that means they won’t be in your lists, but they won’t be downloaded to new players, anyway.
You can always delete challengelist.txt and refresh if you want to ensure they are up to date.