[tempay]

For those not aware: https://en.wikipedia.org/wiki/Pentium_F00F_bug

Can these kind of bugs possible to exploit to cause anything more than minor annoyance?

[hexadecimated]

If it works inside a VM, an attacker could potentially cause a widespread denial of service on cloud computing platforms like Azure and AWS.

[viraptor]

Use them to exploit the system itself - not likely. (Unless they cause some specific bad behaviour rather than a crash) But you can definitely use a DoS issue for other effects. For example if someone is using an auth revokation system which fails open, you could kill that part to use expired credentials. Or if you're able to sometimes inject data, you can keep killing the caching systems until your response is the saved one. (Like in DNS hijack)