Can dogs catch mumps off humans? Has had anyone had any experience of this or has anyone let their dog around someone with mumps that has been okay?

Yes they can, its Anthroponotic to dogs.

'Humans are the only known natural hosts of the mumps virus, although close contact between children and their dogs can occasionally result in canine mumps parotitis. This virus is spread by direct contact via the respiratory route. Infection occurs throughout childhood.
Mumps make you quite uncomfortable but it usually is not a serious disease and rarely lasts more than 2 weeks. In some cases, however, encephalitis may develop which is a serious complication of mumps and can lead to neurological symptoms and, rarely, death.
During adulthood, infection is likely to produce more severe disease.
Mumps infection during the first trimester of pregnancy can increase the rate of spontaneous abortion.  Although mumps virus can cross the placenta, no evidence exists that mumps infection in pregnancy causes congenital malformations. The vaccine is for Measles, mumps and rubella (MMR). Neutralising antibodies against the mumps virus have been shown to be effective at least 12 years after vaccination. To prevent dogs from catching mumps, never let them come in contact with an infected person.'