Different parts of the vacuum system are isolated, so even if there is a leak in one part, not all vacuum-dependent systems will be affected.
The rear headrests going down (particularly intermittently) are enabled by an electrical switch connected to and associated with the rear windshield sun shade being retracted all the way down in its recess. Often the sun shade doesn't go quite down far enough to activate the switch, so you have to press it down in its slot with your fingers. This activates the switch and then the rear head rests will fall "down" into the rear deck below the window when you press the dashboard-mounted headrest switch.
There is an electro-vacuum valve below the rear deck that controls the vacuum to the rear head rests, but it is very very very rare for this vacuum valve to go bad.
As for the transmission shifting harshly and a possible vacuum issue -- that is definitely a possibility, though there are a couple of vacuum connections to the transmission.
The most common issue may be the vacuum line going from the intake manifold down the back of the engine to the modulator on the side of the transmission on the driver's side. You can remove this line and take a look at it to ensure that it isn't melted or otherwise broken / punctured.
Often these old vacuum lines grow old and brittle with age and heat, so it is a good idea to replace them anyway.
You can get at the end of this transmission modulator vacuum line from underneath the car (search the forum for threads on this) and the top end of it is attached to the back of the intake manifold.
