I think that this is standard problem with temporary files - have you tried to exclude this files from check-in process? You can do it in User Settings dialog - Adding Files. Browse Admin Help for this topic - "Settings Dialog Box - Adding Files". You can do it either for particular users/groups by clicking RMB on this user/group and then "Settings", or for whole installation - going to Administration and click RMB on "Users - > Settings".
Let me know if this is good shot or we can search for something else.
The "~" is Wojciech stated. Temp files for when the file is open. IF a crash occurs Windows often doesn't delete them. They can be deleted if not necessary.