None.
The continue restart is generally part of protocols where there is a single "obvious" way to continue, such as in break and cerror. Some user-defined protocols may also wish to incorporate it for similar reasons. In general, however, it is more reliable to design a special purpose restart with a name that more directly suits the particular application.
(let ((x 3))
(handler-bind ((error #'(lambda (c)
(let ((r (find-restart 'continue c)))
(when r (invoke-restart r))))))
(cond ((not (floatp x))
(cerror "Try floating it." "~D is not a float." x)
(float x))
(t x)))) ⇒ 3.0
Restarts, Interfaces to Restarts, invoke-restart, continue (function), assert, cerror