On the air-gapped computer of Diana, Peter could install a driver for a wireless 4G-modem, which should not be possible, since that computer is highly secured.
When Rose packs up her computer and leaves the diner, she neglects to take her power cord from the socket in the wall behind her. However a State Trooper finds it and hands it to her a few moments later, so it is a purposeful plot device.
The gas station sign is a Canadian-style one (only one price visible). US-style ones tend to have multiple prices listed.
When Rose and Peter are at the cabin, the viewer sees a forest full of Western White Pine trees. These trees are not found in the eastern two-thirds of the United States, much less near Washington DC.
Too careless of Rose to go to a diner when she knows the cops have her description, then sit in front of a window, facing most of the customers, making her maximally easy to find. She's much too cautious and untrusting to do anything without minimizing exposure.