A while ago there was a Windows server vulnerability that was due to flaws in previewers that were triggered by search indexing mechanisms run on the server. That allowed an attack that was present in the uploaded media file to also infect the server. Both JPG and TTF previewer flaws were exploited by different kinds of malware. So it's historically been possible for a user provided file to not only attack other users, but unattended servers, too.
These flaws have long ago been fixed, of course. But they're an important reminder to be really careful with uploaded content, because you can pretty much expect vandals to upload infected files.
Older Flash files are known for having serious vulnerabilities. You could try validating the uploaded files, making sure they're a current version. The tool Blitzableiter is a Flash conformity tester that tries to fix dangerous incompatibilities, you could consider testing all uploaded software with it before allowing it to be served.