Dog health?

Dogs and cats can certainly have a localised reaction to vaccines(or any injection) however it would only occur at the sight where the vaccine was given and would happen within one week of the injection.
A soft mobile mass on the leg could be a tumour either malignant or not. Lipomas are benign tumours that develop on dogs, they usually develop slowly over months to years. However a fast growing mass would usually indicazte something more serious. Watch the mass and if it grows rapidly or changes in anyway take to vet for a fine needle aspirate to be taken and they will look at the cyctology of it under microscope. If it looks fatty it will be a lipoma and no need to worry unless it causes trouble for your pet, however if they see cells they will need to send the cytology sample to a pathologist so that they can work out what kind of mass it is and whether surgery is required.
If I was you (and this is what I would tell clients) watch for 1-2 weeks if changes occur in size, shape or the skin near it then bring in, if not keep watch and get it looked at at next vaccination.