My professor uploaded an unsigned recommendation
I wouldn't worry too much about it. 

We're currently in a transitional state between a world of paper documents and a world of electronic documents, and the conventions for digital signatures haven't really converged yet. As such, some people sign on paper and scan, some sign digitally, and some don't sign at all.  If you're dealing with a large institution, they've probably seen it all, and are unlikely to hold it against you.  After all, even if it was signed, what's the likelihood they would actually know what your professor's signature looks like?