MAJOR LESSON: The take-home message from 'The Incredibles' was "No Capes!!". The corresponding lesson from Gravity is: learn your tether protocol. Correct tether protocol would have saved Ryan Stone a lot of grief.
BACK STORY: In order to make sense of the mission of STS-157, we have to assume several back story events:
1. Some crazy person (President Rand Paul, perhaps?) has ordered Atlantis out of mothballs, upgraded, and renamed Explorer. The ET and SRB production lines were also restarted at great expense and pad 39 was refurbished. This solves the problem of why there is an STS-157 at all. 2. As an experiment to do with future exploration plans, the ISS orbit has been raised 200 km. 21 new Shuttle missions, STS-136 to STS-156, were flown to perform this, the HST changes mentioned below, and other missions which relocated various ISS modules to new locations and added the currently-cancelled centrifuge module. This explains the '600 km' at the beginning of the movie and some discrepancies in module locations. The ESA ATV production line was also restarted, explaining why an ATV is docked to Zvezda. 3. In a related experiment, a low thrust engine was attached to HST and and its inclination changed from 28 to 51 degrees over a period of several years; its altitude was reboosted to 600 km in the process. The engine was discarded after rendezvous with ISS was achieved. This explains how HST ended up MMU-accessible from the Station. 4. The Martin Marietta MMUs (retired in 1985) were removed from mothballs in Denver and restored to flight status. This explains why Clooney is flying an MMU. The electronics have been upgraded and miniaturized, leaving room for lots of extra propellant, explaining the additional capability that the real MMU didn't have. However, the SAFER units currently used by the astronauts, which would have saved Clooney and made Bullock's task way easier, were grounded for some reason - it's hard to understand why they weren't wearing SAFER packs, except of course that half the plot of the movie would be gone. 5. As a result of slowly thawing China-US relations, although China has not yet been invited to join ISS as a full partner, an agreement was reached for the new Chinese multi-module space station to also be placed in an orbit stationkeeping near to ISS. Problem: Space debris 6 - In the movie, a dense field of debris is encountered by ISS every 90 minutes. The debris appears to have a number density of at least 1 10-cm object every 10 square meters in a very thin (< 1 km?) plane. We see it coming past, so its relative velocity is really slow by orbital standards, at most 0.1 km/s or so. Since there has not been time for the debris to fill out its orbital plane, its orbital period must be quite close to that of the ISS and it must extend over at least several 100 km or so (to allow for differential phasing). None of this makes sense with the Russian military test explanation provided by Houston in the movie. Also, there must be at least 10 to 20 metric tons of debris. - Solution - Houston is lying for national security reasons. The target, for unexplained reasons, was a 20 metric ton cargo ship (Japanese HTV, perhaps) in the late stages of rendezvous with ISS. This explains the low relative velocity and large quantity of debris. 7. A LEO debris incident won't knock out the TDRS geostationary comm satellite system. - Solution - to pay for the Shuttle production line restart, TDRS has been defunded. ISS now relies purely on Iridium phones and the Iridium constellation is partly disrupted by the debris incident (although it doesn't make sense that you'd lose all comms, that part just doesn't work). 8 - Debris is going retrograde (east to west). - Solution: I'm not sure you can tell this from the views given. It is retrograde relative to the ISS but not necessarily relative to the Earth. That just says something about the sign of the ISS-relative velocity, not the Earth-relative one. Problem: Physics 9. - It makes no sense that Clooney is dragged away from Bullock when he lets go of the tether, since his relative velocity starts out at zero. - Solution: one of the ISS modules is, out of view, venting atmosphere or propellant in an appropriate direction. Clooney isn't being dragged away from ISS, the ISS is accelerating away from Clooney. This explains why Bullock's tethers are under tension, too. 10. - The ISS solar arrays are flexible and should vibrate and wiggle when you crash into them. - Solution - yep, can't solve that one, that seems like a mistake to me. 11. - The astronauts should have bruises and broken limbs from banging into ISS bits at high speed. - Solution: none, this is a problem. 12. - Portrayed as too easy to close the EVA hatch while it is venting. You'd be pushing against a lot of pressure. - This is a problem, but let's say the hatch was already partly depressurized for some reason. Orbital Mechanics 13. The Soyuz DMP soft landing thrusters are used to get to Tiangong. The thrust is sort of plausible but I don't think there is any way to point the spacecraft in the right direction. No solution. Bad Astronautics Practice 14. MMU exhaust plume near Hubble optics would contaminate them. I don't think so, MMU used pure N2 - should not be a problem? Not like hydrazine. 15. No EMU stripe coding - spacewalkers wear different stripes on their suits to tell them apart. Solution: For some reason on this particular EVA a last minute suit change was required and the stripe coding was omitted. 16. Bullock has only 6 months training - she is a payload specialist, not a mission specialist. Solution: We assume that the payload specialist nomenclature has been retired, since she is referred to as 'mission specialist' but clearly she is what today would be called a payload specialist. She shouldn't be doing MS tasks like EVA. We assume that in the restarted Shuttle program, a presidential level decision was made to assume greater degrees of risk, or that some high level political decision was made to allow Bullock to EVA in this particular case. She should have spent some of that 6 months learning about tethers though. 17. Awful tether protocol. For example, as soon as Bullock manages to catch hold of ISS, she should attach a tether (of which there MUST be several attached to her suit) and then 'mountaineer' across the ISS, attaching one tether before releasing the previous one. This would not have slowed her down too much and would have saved her a lot of near-fatal missteps. 18. HST should be deployed by the robot arm, not manually. - I'm not sure if there is an emergency manual jettison method, but there certainly should be. We can assume the FSS/BAPS has been modified to permit one. 19. How did all the ISS crew get home? There are 2 Soyuz still docked to ISS. In normal practice a Soyuz is only attached if it has a crew on ISS. The implication is that we started off with three Soyuz docked, and a crew of 9 squeezed into 1 of the Soyuz to get home - not possible. - Solution: In the future, a decision is made to launch extra unmanned 'rescue Soyuz' ships and keep them docked at the Station. 20. It takes a long time to repressurize the airlock - many minutes, not seconds. - Solution: there is an emergency repress mode on the US airlock, not sure about the Russian ones. 21. It takes a long time to get off your spacesuit, much longer than shown. - Solution - maybe a new model EMU that's easier to get off somehow? And with the cooling garment integrated, explaining why Bullock is in t-shirt and pants, not an LCVG 22. The name of the future big Chinese station will likely not be 'Tiangong', although one of its modules may be Tiangong-2. (Tiangong-1, now in orbit, is a small lab, not the vehicle shown). - Solution: Ignorant American astronauts refer to it by the wrong name out of habit. 23. The Soyuz TMA-14M name doesn't fit the timeline. - TMA-14M should be launched next year. TMA-24M might be more plausible. I'm going to pretend they misspoke and it was actually TMA-14M2, in a new Soyuz TMA-M2 modification of the series. 24. Some people complained that The side hatch on the Soyuz orbital module doesn't exist on flight Soyuz vehicles, but only on simulators. - Solution: These people are wrong. The extra simulator hatch is on the descent module. The hatch on the orbital module is there as depicted in the movie, and is used to get in and out of Soyuz on the ground. 25. Bullock is a medical doctor, as well as apparently a scientist who develops medical imaging devices. Her imaging device has been adapted for use in astronomy. How come she did this? - Solution - she was originally trained in astrophysics, but couldn't get tenure and retrained in medicine. It's plausible that technology developed for medical imaging could turn out to be useful as an astronomical imager, but only after about 10 years of redesign and many intermediate steps, so this is really a stretch. 26. Neil Tyson pointed out that Clooney, a test pilot, lectures Bullock, a medical doctor, on what happens medically during oxygen deprivation. - Solution - I don't find this in any way implausible or unusual. Google "mansplaining".
I hope this sorts things out for you. I acknowledge useful conversations with Alanna Krolikowski; portions of this research were carried out at Stoddard's Food and Ale in Boston. Some of the issues addressed in this paper were raised by @neiltyson, @spaceshuttlealmanac, Garrett Reisman and others; this article is a salute to their nerdery.