How can I get LWP to verify that the certificate of the server I'm connecting to is signed by a trusted authority and issued to the correct host? As far as I can tell, it doesn't even check that the certificate claims to be for the hostname I'm connecting to. That seems like a major security hole (especially with the recent DNS vulnerabilities).
Update: It turns out what I really wanted was HTTPS_CA_DIR, because I don't have a ca-bundle.crt. But HTTPS_CA_DIR=/usr/share/ca-certificates/ did the trick. I'm marking the answer as accepted anyway, because it was close enough.
Update 2: It turns out that HTTPS_CA_DIR and HTTPS_CA_FILE only apply if you're using Net::SSL as the underlying SSL library. But LWP also works with IO::Socket::SSL, which will ignore those environment variables and happily talk to any server, no matter what certificate it presents. Is there a more general solution?
Update 3: Unfortunately, the solution still isn't complete. Neither Net::SSL nor IO::Socket::SSL is checking the host name against the certificate. This means that someone can get a legitimate certificate for some domain, and then impersonate any other domain without LWP complaining.
Update 4: LWP 6.00 finally solves the problem. See my answer for details.