The display is a 240x128 bitplane (30*128=3840 byte) that is per default placed on adress $4440 but can be moved to any even 8 byte boundry. Timed events is accomplished through a timer that is ticking at about 1.6KHz. The timer generates two interrupts, one for every fourth tick and one programmable. The LCD is refreshed every 16th tick of the timer, which is around 100Hz.
The IO-cable, keyboard and ON button generate interrupts as well. An interrupt can also be made to occur when memory below $120 is written.
The TI92 ROM supports sending and receivning backups. When you send back a backupfile that is too large, it will wrap around and start overwriting at adress 0, allowing you to overwrite the vectortable to jump to a routine that was previously put in memory via the backupfile. This is currently the only known way to run your own assembler code on the TI92 (and was discovered by David Ellsworth).
During normal calculator operation, the TI92 is always in Supervisor mode.