Thanks to both of you for your replies! After numerous tests I found that the problem comes from the custom theme we were using. If I switch it off by creating a separate folder install of 1.10 with our current ost-config file, it works just fine.
We're waiting for the 1.14 release to re-haul everything, including a new theme. The business hours for SLA will be a killer feature for us, one that we were hoping for since we started using OSTicket!