I'm running it on Debian (the "testing" distribution), on a Mac with MacOS 10.5 and on Windows XP. There are no obvious differences in functionality, it's stable on all platforms and tends to be slowest under Linux (fastest on the Mac).
Biggest pro in my opinion is security: no malware to worry about, no viruses, etc. You can just boot Linux from an USB stick or a CD/DVD and take this virus-free environment with you everywhere.
Con: changes/updates whatsoever of the Java implementation are critical (in my experience a lot more so than under Windows or MacOS). Otherwise I don't see any
Shouldn't be a problem running it on Linux as the TWS is pure Java. Have in the past been using it on other platforms as Sun Solaris and HP-Unix without any problems.
I don't use charts for real-time trading, so TWS charting capabilities are fine for me (TWS beta has improved and better looking charts as opposite to the latest stable release).