Gravitational waves and gamma ray burst: how were the error bars determined for this speed of gravity calculation? Was $H_0$ used? This newly updated answer to How precise are the observational measurements for the speed of gravity? and this answer to How is the most accurate value of  measured? cites the November 2017 arXiv preprint Gravitational Waves and Gamma-rays from a Binary Neutron Star Merger: GW170817 and GRB 170817A which says that these measurements:

constrain(s) the difference between the speed of gravity and the speed of light to be between −3×10−15 and +7×10−16 times the speed of light.

What are the major assumptions and other measurements that went into these error bars? Did they use a range of values for the Hubble constant? Was the dispersion of the interstellar medium at optical frequencies included? Were known limits to the variability of fundamental constants also applied or were those assumed to be constant? Anything else?
We don't often see uncertainties in the 10-15 range in Astronomy! :-)

Potentially related:

Have more recent LIGO/VIRGO gravitational wave measurements narrowed down the speed of gravity further?
Have there been studies of &quot;old photons&quot; to see just how constant things like Planck constant has been?
Are photons aged?
What are the major assumptions and other measurements that went into these error bars?

The error bars in the paper are based on the shortest reasonable distance (to the authors) between the source and the Earth and a zero to ten second lag between gravity wave emission and gamma ray emission.
One key assumption is how long it took for the two signals, gravitational wave and gamma rays, to travel from the source to the receiver (the Earth). The 1.74 second difference in timing of the arrival of those signals would mean the speed of gravity and speed of light would be nearly identical if the signals traveled a long time (long distance), but maybe not so little if the signals traveled a shorter amount of time. The authors of the paper intentionally picked what they deemed to be the shortest reasonable light travel time (shortest reasonable distance) so as to magnify the uncertainty bars.
Another key assumption is that the two signals were emitted very closely in time, with the photon burst following the gravity wave by no more than ten seconds. The authors alluded to fringe theories that had the photon burst preceding the gravity wave emission by a non-trivial amount of time, and other fringe theories that had the photon burst lagging behind the gravity wave emission by much more than ten seconds. The paper mentions these only in passing.

Did they use a range of values for the Hubble constant?

The Hubble constant does not come into play here. The authors used what they deemed to be the shortest reasonable distance (the product of travel time and the speed of light) between the source and the Earth, based on luminosity.
Note that at 26 Mpc, the Hubble constant is not particularly relevant.

Was the dispersion of the interstellar medium at optical frequencies included?

Apparently not; this is a simple calculation. Moreover, dispersion at optical frequencies is rather irrelevant as the observations were of gravity waves and gamma rays.