The hazards of slips in a swept wing airplane have been touched upon, but there are issues beyond control to be considered. A control reversal has been mentioned, but in the sense of a pilot rapidly reversing control inputs. This can be dangerous, but an aerodynamic reversal may also occur.
I've slipped one turbojet airplane, and technically I didn't do the slip. It was an individual with me who did the slip, whom I quickly corrected...and he performed a full slip without any announcement regarding his intent, when he found himself high on approach. That was in a barely-swept wing (a Lear 35, which is also a very strong airframe). In a highly swept wing, a slip offers far more disadvantages than advantages...which is part of the reason we have high-drag or lift-killing devices on many airplanes, rather than simply performing slips.
I've done full slips in large four-engine airplanes on many occasions while performing low altitude maneuvering as part of aggressive firefighting activities. However, I stopped doing it when I learned about the after effects. The use of the slips was commonplace among most performing that type of work at the time. However, as most of us were also mechanics/engineers and were involved in performing the inspections on the airplanes as well as flying them, we had opportunities to see far more of the airplane than most pilots. During heavy maintenance checks, I began to see damage to attaching brackets, surfaces, and bolts, primarily on the vertical stabilizers.
Most pilots would be rather shocked, I imagine, to find out just how little holds the vertical stab in place on many aircraft. Then again, many were shocked to find that the vertical stab left the aircraft during a pilot-control-reversal in American Airlines 587, too. In our case, some of the aircraft had very little, and very small bolts attaching the vertical stab...and not so many as one might expect...and we were finding them cracked.
The side load on the vertical stab is significant, as is the torsional or twisting moment when large rudder deflections are applied. As airspeed increases, this load increases in the sideslip. Unlike a wing with a spar that's intended to take a load and a bending moment and has wing root support through the spar, attach points, and additional member, the vertical stab was simply designed to help align the aircraft with the slipstream. It's a stabilizing surface, not a lifting surface,and was never intended to be exposed to the types of loads that repeatedly slipping the airplane can impose.
That brings up the question then, can one simply slip it once and be safe? Setting aside the aerodynamic effects of slips in a swept wing configuration, one must ask just how strong is that vertical stab? Even if the vertical stab is strong, what about the attach bolts? What about the brackets? Do you really want to find out? How many times has it been slipped before, and under how much stress have those components been placed in the past? Have the bolts ever been inadvertantly overtorqued, and the fittings and bolts themselves ever been exposed to over-tension? Who's to say?
We were finding cracked fittings and bolts and had no idea at what point the failures had occurred. Just barely, or some time in the previous 100, 200, or 300 hours? We didn't know. What we did know was that the evidence clearly indicated that full slips in the airplanes was contraindicated; a bad idea.
We did full slips because maneuvering close to terrain (down canyons, in mountains, etc) was a job function, and slips were preferrable to flaps. A slip can be ended instantly, restoring performance, whereas changing aircraft configuration with flaps or gear takes time...time which one might not have inside a canyon or variable, steep terrain. It worked very well, too,and was very effective in accomplishing the mission we had before us. After I began to be exposed to the after-effects, however, I elected to find other ways to accomplish the same mission.
Some airplanes are subject to other types of control reversals than simply pilot-applied changes in the direction of control input. In the C-130, for example, a control reversal or more correctly a loss of authority could occur with "fin stall." Over-deflection in a slip could lead to loss of rudder authority, and ultimately result in the aircraft yawing farther into the slip. This is not the case on all aircraft, and even on the same aircraft it's not the same in all scenarios. A combination of angle of attack and sideslip, such as in a steep descent, can cause combinations of airflow disruption, separation, or loss ("blanking the tail"), and this can in turn cause the rudder (and elevators in some cases) to lose effectiveness, or even cause the vertical stabilizer itself to lose effectiveness. Flaps can also play a role in such a situation.
Many years ago I worked in the shop for a company that flew 30 or so Cessna 207's. A far cry from a large, swept-wing turbojet airplane, these were simple, strong airplanes that were primarily used for tours, for back-country charter, a lot of dirt-runway and rough field work, and all in the mountains. When flying the airplanes, the use of slips was very common. However, over a period of time, I began to find the vertical stab attach brackets broken...on all the airplanes. Eventually a fix was found and most 200 series airplanes have improved steel attach brackets now. Over the course of a single year, I found nearly every attach bracket broken on those airplanes, until they were upgraded and pilots were encouraged to stop slipping so much.
I mention that because even a small, light airplane which is commonly slipped can face structural problems, and there's nowhere near the load on a small airplane as there is on a large airplane. However, as the airplane gets bigger the proportion of the attach bolts and brackets doesn't increase accordingly. Big airplanes have bigger brackets, bigger fittings, bigger bolts...but not so much as you might think...and certainly not in proportion to the increased area and loads that can be developed in uncoordinated flight.
Add to that the uneven airflow into engines, the potentially drastic change in airflow over swept wings, and controllability issues, there's little to be gained. When one slips a swept wing airplane, one isn't increasing drag so much or losing lift; one's transferring it from one wing to the other. If one applies spoilers or speed brakes, on the other hand, one is increasing drag, and this is far more effective.
Another consideration for performing a slip at a time such as an emergency descent is control authority and deflection. Performing a slip at high altitude from cruise speeds may not even be possible. In the B-742 for example, our controls are locked out with only the inboard ailerons available, and rudder travel is limited; we can't put much control authority into a slip and can't create much of a slip. There's a lot of wing out there to twist and flex, and the outboard ailerons are locked out for this very reason. The whole airplane flexes to a much greater degree than many people realize, anyway, and bending it around even more isn't in anybody's best interest.
I submit that slips are best left to supercubs, but I submit that slips aren't so good for supercubs, either. I've been flying ag airplanes and fire airplanes along with other bigger equipment for many years now, and I won't slip an Air Tractor or a Dromader into a fire or over a powerline, either. I used to...but having seen what I've seen from a mechanic's perspective, those days are past.