curl 7.62.0 through 7.70.0 is vulnerable to an information disclosure vulnerability that can lead to a partial password being leaked over the network and to the DNS server(s).
curl 7.20.0 through 7.70.0 is vulnerable to improper restriction of names for files and other resources that can lead too overwriting a local file when the -J flag is used.
A malicious server can use the FTP PASV response to trick curl 7.73.0 and earlier into connecting back to a given IP address and port, and this way potentially make curl extract information about services that are otherwise private and not disclosed, for example doing port scanning and service banner extractions.
A non-privileged user or program can put code and a config file in a known non-privileged path (under C:/usr/local/) that will make curl <= 7.65.1 automatically run the code (as an openssl "engine") on invocation. If that curl is invoked by a privileged user it can do anything it wants.