This has been reported for both the 1985 Cold War Crisis and the Red Hammer campaigns. Before you read on, have you check your system's available memory and Windows virtual swap file size? Read about that over here.
OFP player MonkeyGoat tried every previous solution mentioned for CTDs (crash-to-desktop) here in The FAQ and elsewhere but nothing seemed to work. Then he mysteriously tried uninstalling the CloneCD utility from his system and - presto - the problem disappeared. Since making this discovery, other players have had similar success.
On the other hand, player MaxDamage had the same problem but he had NeroBurn installed on his computer - not CloneCD. He completely uninstalled NeroBurn but that didn't help. Then he installed (yes - installed!) CloneCD and the problem disappeared. Go figure!
Do you have the same CTD problem but don't have CloneCD installed on your computer? Maybe another CD burner software utility is causing the problem. If you discover another product that, when uninstalled, resolves CTDs at mission completion in Red Hammer, let me know and I'll update this item for the benefit of everybody.
Now, what's still bothering me is what connection is there between CloneCD and Red Hammer missions completing? I can understand the connection between CloneCD and OFP startup, installation or upgrading - these are all processes where OFP accesses the CD. Got any theories that can help explain this phenomena? I'm all ears!