So this morning, after my short drive to the train station, when I shut down the car, I got a message on the OBC that said "Taillight out". Which is fine, because my gf pointed out the other day that one of my reverse lights was out. So that's not a big deal. It just never gave me the onboard warning before. However, it also said "Check Coolant Level & Check owner's manual". The coolant warning is the one that has me concerned. Never seen it before. Right before I picked up the car, the previous owner and his dad (both BMW mechanics/fanatics) had flushed and changed the oil/coolant. I popped the hood and there was no leaking, hissing, steaming, visible drips, etc. The temperature gauge was fine - it was still towards the "cold" side and hadn't really had time to warm up on my 5 minute drive to the station.
Did some googling and haven't really found anything too useful other than some people saying that the sensor can occasionally be faulty/erroneous.
Obviously I'll keep an eye on it but I'm just wondering if there's anything else I should be checking for/worried about. As I said, I've never seen any warnings on the OBC at shutdown before so that was a little weird.