CAN bus signal integrity
No. The differential signalling is performing as intended.
No. As long as the "common mode voltage" does not exceed the ratings of the transceiver. And the maximum DC ratings, which for a CAN transceiver like the MCP2551 is -42&nbsp;V to +42&nbsp;V.


The twisted pair cable and the differential signalling mode make the single-end signals look like gibberish while the differential signal is not affected by the noise. You will have the occasional corrupt frame, but CAN has several features to ensure only correct frames are accepted and bad ones are re-transmitted.


CRC to detect bit errors.
Error frames. When one node detects an error, it sends an error frame, and this frame forces the bus dominant longer than the bit stuffing rule. All nodes see this.
Automatic re-transmit until the error limit.


I have one of these images as well. These are textbook images on differential signalling. This kind of noise is inevitable in systems with electromechanical or high power switching components.