A few things pop into my mind. All sorts of weird things happen to the RL when the battery isn't giving the proper voltage. If you have resetting trip meters and all sorts of these electrical issues, I'd say you either have a loose connection on the battery itself (as stated by Qxtreem) or you have a bad cell within the battery itself. Even brand new batteries can be bad. Plus, you never know how long it sat in a production lot, on a transport truck or on the dealer lot. Being that it's winter and has been very cold, it's possible that the battery in the truck died while on the lot and it was recharged before you bought it. Once a typical non-AGM car battery completely looses charge and is recharged, it is never the same again and will fail much sooner than normal. Bottom line, take it back to the dealer and have it looked at under your warranty. Have them do a load test on the entire charging system to rule out things such as the starter and alternator. Also have them check every power and ground lead for the charging system to make sure everything is tight and secure. If the load test of the battery shows anything less than 90% or so of its rated CCA number, replace it. The stock battery that comes in the RL is pretty weak, so I would recommend you trying to get the best battery you can if the dealership offers anything better than the stock one.