The up arrow should be lit up when you 'dis-engage' the Overdrive. That is supposed to be for when you are towing a trailer or driving in a very hilly area. It isn't used by about %95 of the people, but it causes problem. It isn't uncommon for the relay for it and/or the Solenoid for it to go bad. If you start the car, the light should be off. When you press the little button on the side of the shifter handle, it should light up. If anything different then that is happening post back and I or someone else will walk you through it.
I would have to look on my 240 to see what the other light is, but I am betting (without looking mind you) that it is the 'bulb-failure' light. These cars have a ciruit that checks the resisitance for the lighting circuits. When a bulb is out (or a wrong bulb is installed) the light will light up on the dash. IIRC, 240's do have a bit of a weak spot with the circuit board for the tail/brake/reverse lights. Another comon problem is that people use a standard American replacememnnt bulb (1156 or 1157) in place of the European light bulb. When the car sees the different resistence, it thinks a bulb is out. In my opinion, the best way to get around these two issues at the same time is to go to a good auto store and see if they that the European bulbs in stock. If so, take out the tail light circuit board, bring it into the store and buy all the bulbs needed for both sides at once. This way, you are sure that the bulbs are right, you aren't messing around with the circuit board all the time and when you are done, it should cost less then $20 for peace of mind.
Should you care to diagnose the problem before buying all of those bulbs, just turn on all of the lights and walk around the car. Make sure all are working. If you'd like, you could turn on one thing at a time until the 'bulb failure' light comes on, then you'd know what circuit your problem is on.
I hope that gives you an idea of where to start. And, of course, Welcome aboard!
Again, if you replace all the bulbs and there is still a problem, post back.