I have been getting the 'File only saved locally, not to server' error today, and after checking Build Automatically, Work Offline and that the classes were listed in the project metadata listing, I deleted my project and created a new one. No difference.
I did discover, however, that the file(s) will be saved to the server if they compile/have no errors -- it's just that the errors, if there are any, do not appear in the Problems pane with a line number - the Problems tab indicates 0 errors, xNumber of Warnings, etc. and the little yellow warning icon appears at the top of the file and in the Package Explorer.
Any thoughts on this, aside from reinstalling the Force.com IDE itself?