How to use atmospheric discontinuities to blow stuff up!
Engine and rocket designs assume that the atmosphere is relatively homogeneous at a given altitude and that there are well understood continuities across altitudes. Sure, there's some variations in atmospheric pressure, moisture content, elemental composition and temperature but the ranges are well understood and well accommodated in current designs. We do this by forcing piston, jet and rocket engines to handle atmospheric discontinuities beyond their present design parameters and experience "rapid unplanned disassembly events"!
Too much Oxidizer
If an engine, piston or jet, were to encounter higher than usual oxygen concentrations, it could cause the engine to overheat and/or disintegrate. It's not very common to inject high concentrations of oxygen gas into an engine. However, there's lots of information on nitrous oxide which does a phenomenal job of making lots of oxygen available for detonation/combustion.
From Tuner University:
The danger with nitrous, is the same as a turbocharger or
supercharger, if you pack way too much air/oxygen in with not enough
fuel, temperatures can sore inside the cylinder and cause components
to melt/warp. To avoid that problem, we simply make absolutely sure
that the air/fuel mixture is relatively rich (lots of fuel to keep
things cool) and we do everything we can to avoid pre-ignition by
running conservative ignition timing of either stock values or
slightly "retarded" values. (emphasis mine)
AgentJayZ owns a jet engine maintenance company in Canada. His comment on this video indicates that
After burning a few hundred gallons of Jet A, in your afterburning J79, it's a good idea to let things cool down at flight idle before shutting down.
Turbine blades and other hot parts last longer if the temperature gradient within them is kept as low as possible.
Suddenly increasing the amount of oxygen in an engine is equivalent to running it too lean. Given that jet engine temps can reach 2000 C and the special cooling that needs to happen to overheat conditions, anything that will force the engine outside its designed thermal profile will at best cause increased wear and at worst cause rapid unplanned disassembly.
Turbulence (Air velocity discontinuities)
While piston engines and rocket engines won't care as much, turbofans and turbojets will care a lot about inlet turbulence because of the potential for compressor stall.
Per Wikipedia on causes for compressor stall:
Turbulent or hot airflow into the engine intake, e.g. use of reverse thrust at low forward speed, resulting in re-ingestion of hot turbulent air or, for military aircraft, ingestion of hot exhaust gases from missile firing.
Hot gases from gun firing which may produce inlet distortion; e.g., Mikoyan MiG-27.
Air Density Discontinuities
Rocket engines, solid or liquid, don't require external air to run. However, if a speeding rocket hit a pocket of unusually dense air, it may induce structural instabilities in a rocket leading to spectacular failures.

Of particular interest is the parameter, max Q or maximum dynamic pressure is a significant design parameter that engineers must design for. SpaceX talks about it during their launches (Video, just before Max Q). If a rocket were designed to withstand a max Q of 100,000 N but hit a large pocket of denser air, the compression on the rocket could easily cause it to disintegrate.
Given:
$$q= \frac{1}{2} \rho v^2$$
For example (Engineers Toolbox):
- $\rho$ at 15Km is about $.198 \text{kg/m}^3$
- $\rho$ at 5Km is about $.7364 \text{kg/m}^3$
...for a 3.7x increase in density. At low altitudes high density air isn't a problem because the rocket isn't going very fast. The inverse is true at high altitudes.
Air density discontinuities are especially dangerous for rockets given the speeds at which they operate but hitting a suddenly dense pocket of air in any kind of airplane is going to make things uncomfortable.
Human Physiology
These kinds of atmospheric aberrations probably won't do much to a human. Maybe knock them over with turbulence or make them short of breath for a while. Generally, humans aren't operating near their physical maximums where a few percent increase in oxygen or extra pressure while they breath is going to do much. Although I recently learned that NASA doesn't consider any O2 concentration over 30% to ever be safe.
Now, a climber on Mt. Everest is very much going to care how much oxygen he has because there's so little to begin with. Someone on the shores of the Pacific won't care nearly as much.
Yeah, this is all great but how....
How to induce these kind of atmospheric discontinuities is outside the scope of this question. As Earth's atmosphere tends to homogeneity, so it would take some thing, some where, doing work to lift large amounts of air higher in the atmosphere or injecting pockets of high concentration oxygen.