Lately when I first start up and all the lights on the dash come on I see the triangle with the exclamation point (I don't remember seeing this before). It goes off when the rest of the warning lights go off. Today I backed the car out of the garage and put it in park and turned it off. When I opened the dirvers door it beeped, beeped, beeped (like it was backing up). I shut the door and opened it again and it beeped again. I got out and locked it and went in the house. I went back out and unlocked it and opened the passenger door and it didn't beep anymore. I haven't tried the driver door yet. Any ideas if these are going to be problems?
First that warning light is normal. It should disappear in a second after you start the car. My guess is that you didn't turn off the car. Maybe you thought you did, but the car beeps when it's on and the drivers side is open.
That all seems normal. The slowness of the lights to go away might be due to the recent low temperatures. Note: If, from the OFF mode, you press the power button twice with your foot OFF the brake, you'll see all the lights come on. Then if you put your foot ON the brake and push the power button the lights will go off and you'll be in READY mode. You might want to get the 12V battery checked to make sure that it's okay. The 12V battery doesn't fail in the Prius like it does in a conventional car (e.g. Works until can't start so you replace it). Instead various odd things happen that you wouldn't ordinarily think of the 12V battery being the cause of.
Yes Ursle is right, there is a low battery warning that will cause the system to beep when the fob tells the car the battery is getting low. This is so you have time to get a new battery before your smartkey function stops without warning.