Generally, applicants are allowed to keep their shoes on. However, federal polygraph examiners often use a seat pad that may detect changes in pressure that might be associated with such a countermeasure as pressing one's toes to the floor, or pressing a toe against a tack in the shoe or sock.

Thus far, I've only heard one report of a polygrapher instructing an examinee to keep his mouth open during the in-test phase. It was a CIA polygrapher conducting a pre-employment polygraph. See the discussion thread, CIA Polygraph Counter-Countermeasures.