"The close door button on elevators is just there as a placebo."

This is just flat out wrong. ASME A17.1 requires that an elevator have a functional 'door close' button, because the 'door close' button is critical to phase II fire service. However, in normal operation, frequently the 'door close' button does have no observable effect.

Also...

"The pedestrian crossing button is just there as a placebo."

Much like the previous myth, it's not that they're placed there as a placebo, even though they frequently found in a state of disrepair. Pedestrian crossing actuator buttons are crucial to certain specific crossing scenarios.

For example, here is a traffic signal protecting a pedestrian crossing across a 4-lane state highway: http://g.co/maps/rp894 The light remains green to traffic except when actuated by pedestrian demand. Note that this does not mean that when the button is pressed, the light goes to a yellow/red state immediately. Rather, it is programmed on a roughly 1-minute green cycle that is automatically recalled if there is no demand to cross. Pressing the button places that demand. Perhaps it is pressed at the top of its cycle, and the pedestrian will wait up to a minute to cross, or perhaps it is at the bottom of its cycle, and the light will seem to immediately go yellow then red. It actually is quite similar to how inductive loops are often placed in the road to activate traffic lights. At the end of the day both are just a sensor input that indicate cross-traffic demand.

You can immediately identify an actuated traffic signal that implements recall whenever a pedestrian countdown timer goes back up after counting down to 0. This means that the controller received no calls requesting a change to a conflicting phase (either from a vehicle sensor or a pedestrian button), so the controller went back to the top of its phase. Motorcycle riders understand this all too well, as some sensors fail to detect the bike, so if the controller does not automatically "max out", it simply stays red forever on the cross street (or until a heavier vehicle sets off the sensor). There are aftermarket products that are basically magnets that attach beneath bikes to increase the odds of triggering the sensor.

A second more conventional example from another nearby highway: http://g.co/maps/r6h4p Pressing the pedestrian button here invokes a dedicated pedestrian phase. Regardless of the pedestrian's direction of travel, the pedestrian actuator calls for a dedicated pedestrian phase. That's right, red balls in all four directions, for almost a full minute, while pedestrians are given ample time to cross all 8 lanes of traffic (3 through lanes in each direction plus two left turn bays). There is a minimum green time which prevents someone from simply pressing the button over and over again to grind traffic to a halt.

Before someone cites a counter example in their area where a pedestrian button has no observable effect, I acknowledge that this myth is exacerbated by the sheer number of legitimately dysfunctional pedestrian buttons. However I assure you, the engineer that called for them to be installed did not do so simply as a placebo.

That reminds me...

"Flashing your high beams at a traffic signal will cause it to change from red to green more quickly."

This is a bastardization of the actual functionality of emergency vehicle preemption systems. In areas where emergency vehicle preemption is used, emergency vehicles are equipped with a special strobe light emitter, usually seamlessly integrated into the roof-mounted lightbar, that rapidly pulses a coded signal. Detectors mounted nearby are triggered by the coded strobes. Early preemption systems, specifically to the best of my knowledge only the first generation "Strobecom" by Tomar, used uncoded strobe pulses. The first generation Strobecom detectors were incredibly unsophisticated and did in fact respond to consumer strobe lights provided the strobe was synced to the correct flash frequency (IIRC 12hz or 14hz but I may be wrong).

Of course, most municipalities don't use that specific vulnerable preemption equipment. The Opticom system by 3M is by far the most popular, and all generations of the Opticom used pulse code modulation. Modern Opticom emitters go a step further and actually transmit a vehicle identifier that is stored by the controller providing an audit trail later on.

But back to the gen-1 Strobecom, the obvious question is "can't you just flash your headlights at the correct frequency?" And of course the answer is hell no you can't. Even if you were able to consistently activate the high beam switch 14 times per second precisely, a) the headlights emit mostly visible light and the sensors use infrared filters and b) the filaments in the headlights take time to completely light up or go dark; it is not an actual strobe effect.