Periodic refresh of the display will ensure that the incorrect bits that occur due to undetectable noise or other random events are present for a short enough time that they'll not be readily noticeable. Errors will be of a single-bit at a time, and the way in which they appear on the display is unlikely to bring about confusion of, or even notice by the viewer. As the refresh rate is decreased, the likelihood of notice increases, but only by a critical viewer.

Since the purpose of the display is probably to convey information, and not to present perfection, it's quite likely that the purpose will be satisfied, though perfection may not. There's no point in allowing "perfect" to become the enemy of "satisfactory."

If there's only a short signal path between the source of the data and the serial drivers, there's not much risk of falling victim to noise and other random events. However, if there's a long signal path, then perhaps a bit of waveform processing might help, e.g. slowing the rise and fall times on clock and data, decreasing their impedance, AC-terminating them, and, perhaps modifying the timing relationship between them. A schmidt-trigger receiver at the destination will steepen the rise and fall times of the clock and the data as needed to satisfy the driver requirements, but will also have its effect on when those occur, so that must be taken into account. If it's really critical that the signaling be exact, then modulating the data with the clock and separating clock and data at the destination might be worth considering. In such cases, the data/clock relationship is preserved, though there are other considerations.

I'd guess that periodic refresh would be the most easily implemented solution.

RE