Can you get raccoon roundworm from using soap to wash face from a soap dispenser used by someone who washed there hands after touching dirty dog paws?

No: Assuming you know how to wash the face with soap and thoroughly rinse with water, then there shouldn't be concern. The mechanical act of cleaning the face and rinsing with water will remove any parasites and ova from the skin surface, despite whatever may be in the liquid soap (unless the soap was ingested, which would be a troubling thought). Hope this helps.

Not likely: Baylisascaris procyonis is a roundworm that lives in the intestines of raccoons. Raccoon can transmit infection through eggs passed in it's feces. If people ingest eggs from soil or water or items contaminated by feces they can become infected. This type of infection is extremely rare.