Please post the contents of the fml-client-latest.log file inside the logs folder inside your .minecraft folder to some pastebin site and link to the post here.
Note that this log will only contain information on the last time you started Minecraft, not any previous runs.
Hm, that log doesn't mention the ReplayMod, so it's probably not recent. Let's try the Game Output as shown in the launcher (not to be confused with the Launcher Log; i.e. the Game Output log should mention the ReplayMod) instead.
Idk. The duplicate mod is what's causing the recording to fail. I can't tell you whether there'd be other things that'd cause problems as well if the other problem did not exist.