Digital outputs are a simple ON/OFF type of signals that can be used to control annunciators, lights, relays, power lines, flags - that is, all two-state output devices that are present in every aircraft cockpit.
Undoubtedly, the main purpose of digital output signals in you cockpit is to control all annunciators and various mode indicators.
Note that some indicators in your cockpit do not require receiving any data from the simulator for their operation. Often this can be an indicator that only shows the current switch position/state (not the system state!) and can be directly controlled by this switch, as most "korry-type" push-button switches).
When controlling the "On/Off" type of output device directly with controller pins all you should worry about is its power consumption. According to AVR tech spec, the maximum ("damage") current for a single pin in output mode starts with 40 mA, that is quite enough to drive most LEDs used as indicators. Likewise, any other directly connected device (actuator, integrated circuit, relays, etc) should sink the current no more than 20-40 mA.
Powerful output devices that have high-voltage or high-current consumption cannot be controlled directly from microcontroller pins, you should always use some kind of buffer circuit for such devices.
This can be a PNP transistor, a MOSFET or a relay. If you use a relay, make sure that it has buffered input itself (as mentioned above) or it's a low current relay having a coil with higher resistance:
So, any Mega2560 pin can be used as a single digital output when one output pin controls one LED. If your panel has just a few annunciators, you can simply connect the LEDs (or other digital devices) directly to Mega2560 board output pins, taking in account some limitations as described above. This is a simple, but inefficient method.
Same as for direct outputs, you can use a serial output as "On/Off" control signal for other circuits, relays, MOSFETs, etc.
For this, instead of LED, use a pull-up resistor 1k connected to +5v bus and use this terminal as output pin for digital control. In the picture you can see that output terminal #16 is used as digital output (all others can be used either for LEDs or digital outputs as well).
Though no doubt that using 16-bit LED drivers is more efficient and doesn't require a lot of current-limiting resistors as in case of simple shift registers, you can use 74HC595 8-bit shift registers if it is more appropriate for you (for example, you have completed modules with lot of common-cathode LEDs).You can extend a digital output using up to 8 registers in series, or just one chip if you need to have only 8 outputs on the selected pin. When using HC595 ICs you need to connect each LED to the register output terminal with a resistor in series (resistor can be 300 Ω to 1 kΩ ). Three input signal lines - PIN, D and L are connected the same way as for LED driver described above.
You can just buy several HC595 register ICs (about $1 for 10 ICs) and simply wire registers directly to the panel LEDs or make a printed board. The wiring diagram is here in the picture.
Another option is buying breakout boards with 74HC595 registers. You can find sample links on the "Components" page. All you need is to solder LEDs with resistors to the board outputs.