Is it ever safe to have 14 gauge wire anywhere on a circuit protected by a 30 amp breaker?
If the #14 or #12 wire is a branch going to specific loads, then it is "safe" with respect to that load.  It won't overload that wiring regardless of the breaker capacity use (or even if the breaker is bypassed entirely).  However, this is unsafe in the context of changes in usage.  The electrical code focuses on safety and rightly prohibits this.  The circuit breaker is required to be sized to protect all wiring in the branch circuit it feeds to (and the receptacles, too).  This is because someone could overload the circuit (for example plugging in a 12 amp appliance in one outlet and another 12 amp appliance in another outlet on the same circuit, which should trip a 20 amp breaker and would not trip a 30 amp breaker).

In USA, all 15 amp receptacles are actually rated at 20 amps (just not configured to accept a 20 amp plug).  So if you have 20 amp wire (usually #12 if the special cases requiring derating do not come into play), you can use a 20 amp breaker (one more exception in the code is if the branch circuit has a single dedicated outlet, it must be protected at the outlet designated amperage).

Since the normal type of outlets don't have a 30 amp capacity, you can't use a 30 amp breaker on them even if you have 30 amp wiring (usually #10), and meet the electrical code.  The receptacles can overheat, too.  You may need to split circuits if this branch is pulling too much current.