For example I rebooted a host, and it didn't come back. For 10 hours it was down. After getting in touch with their support I was told "Oh yeah, there is a problem with the hypervisor, we'll fix it". Meanwhile their status-site showed "zero problems". (The next day it came back.)
Provisioning a stock (Debian) system results in a host with no working serial console, which makes it hard to rescue.
You can't make outgoing SMTP (25/587) access without giving them copies of passports, etc. Though if you enable IPv6 you'll soon discover outgoing SMTP works ;) Only downside there is you can't set reverse DNS for your IPv6 address.
(Reverse DNS? They require the forward address to point to you before they'll let you set it, as a "security measure".)
I'm using the host for offsite monitoring, but we'll see if it stays. Cheap, but perhaps too cheap.