Any possible danger?
I am not a computer expert, nor a coder, and not particularly knowledgeable about such things and I love Zotero (having used it throughout college and now in grad school). However it has occurred to me that it could be a clever front for some sore of spy program to steal important information. Is this at all possible?
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Like any software that interacts with websites, when you use Zotero to download files, if a file contains malware, Zotero will copy the file. Your protection against that malware is your operating system and any security software on your machine.
I've used Zotero for a decade. My work requires visiting both well-known and very obscure book and journal publisher websites and downloading many hundreds of files each day. I download technical documents from agencies and organizations throughout the world. (I use Zotero primarily as a MODS translator instead of its intended use as a research and writing tool.) I doubt if anyone consistently downloads more metadata or files via Zotero than I do -- more than 10000/week, every week. All without any Zotero-related problems.
That said, if you are employed in a setting where there are tight controls on the security of highly confidential files, you may want to ask specific questions about those issues.