If the grid goes down, there are back-up generators. But usually there is sufficient fuel for only a few days. However, nuclear fuel requires that cooling water be circulated for several years. Chemical plants, refineries, and pipelines have many embedded systems. I believe that dangerous plants that have not been repaired, and the repairs tested by an independent party, should be shut down for the century change, and restarted very carefully thereafter.
Manufacturing is vulnerable to a shortage of parts.
Shipping is threatened by a late start and because many ships are based in countries which have not been working on y2k. Modern cities are made possible by water treatment plants and sewage treatment plants. These plants use embedded systems and require electricity and telecommunications. If utility systems fail, high rise buildings could become uninhabitable. If heating systems fail for several days in the winter, pipes may freeze.