The main inconvenience for me is probably having to use multiple keyboard shortcuts when copy-pasting between different VMs, but that should not happen very often anyway ;-)
I also have issues with shutting down the machines from time to time - it gets stuck in an infinite loop when disconnecting the LVM volumes or something. (Probably should have reported that to the devs long time ago, so I'll see if 3.2 fixes this and will report if not.)
Obviously, whether Qubes improve/solve your security problem is a complicated question and it depends on your threat model.
Update: Actually, I've just remembered another inconvenience - I haven't managed to install zfs (zfsonlinux) to get working inside VMs. It needs to install custom kernel modules, and the location is r/o by default. I've found some instructions on the mailinglist, but haven't managed to get it working.