Had to create a plugins subdirectory. Downloaded and extracted jre-7u17-linux-i586.tar.gz, found the mentioned file and copied it into plugins/. Restarted firefox, brought up Proxmox server page, selected a CT, clicked on "Console".
Same result as all attempts before: After approving the code to run, I get a window with black background except for a highlighted backtick in upper left. No OS prompt. Can type in the window, but no response from any system.
Same result on many student laptops running Windows (I'm running Mint Nadia). Same result on my laptop when using the update-sun-jre package from duinsoft. Same result in Chromium (FOSS version of Chrome browser).
I cannot play around too much with Java JRE on my laptop, as that is the language my department uses for instruction, and I need a working JDK to teach classes. I also have work to do, much as I might enjoy messing around with under-the-hood software configuration workarounds.
The only way I've successfully accessed a Proxmox CT or VM console is to use VirtualBox to create a virtual machine on my local laptop, download, install, and configure Oracle JRE 1.6 (didn't try 1.7), and run Firefox in that virtual machine. Rather a bit of overkill just to get a console, and not something I can reasonably ask/expect all my students to do unless I'm willing to do personal tech support for all of them, with all their different OSes and browser configurations. And if I modify their machine's Java to work with my courses, I have to worry about breaking something they need for another class (or real life).
That is why I'm heartily in favor of Proxmox moving to a VNC implementation that really does "just work". Proxmox is a great system, but what students are learning from first-hand experience can be summed up as: "cool idea, major hassle".