Do the parts in question happen to be linked to another family? That was my problem. After the 2011 install, I got the same error with some of my components and after searching and looking around and stuff, I eventually broke the links from the original family that the components were made from. For whatever reason, all my CC parts work fine now. You may just want to look into that as a solution, backing up your CC first of course in case you would want to return it to the normal state.
Just throwing that out there.
I would recommend you try saving a CC part from a family you are having problems with using the 'As Custom' option and save the file to your Work Space. If you are successful doing this then I would suspect you do not have the correct permissions set for the directory you are attempting to save to with a 'Standard' CC part. I have seen the 'Unable to create Part' message previously if your Inventor directory for CC parts is located under the Program Files directory.
Hope this helps, Paul
I have had the exact same error message come up for me in the past. I am on Vault though. My barbaric solution was to find the part and delete it in my Vault and then I was able to reinsert it into my assembly.
Probably does not help you because it sounds like your user is not using vault.
Wild Shot..... do you have Excel installed (what version please)?
Can you create an iPart?
I had the same problem when I tried to place a content center part into an assembly, but I have located my prolem and that is empty fields in the Family table. I have created my own customized cc-parts and added an column with ordernumbers and not every dimension has one so I left them empty and that resulted in "unable to create component" for those who had empty fields.