The study of gamma-ray bursts and soft gamma-ray repeaters is advancing rapidly, as the many recent discoveries discussed by Fishman (1995), Paczynski (1995), and myself make clear. However, as I stated in the Introduction, there are many reasons why the answer to the question of the distance scale to gamma-ray bursts still eludes us. Below I mention several key observations that might help answer the question.
Sky distribution. Our ability to detect or place upper limits on any anisotropies in the burst sky distribution, especially as a function of burst brightness, will increase slowly but steadily as BATSE detects more bursts. Confirmation of significant Galactic dipole and/or quadrupole moments as a function of burst brightness, or overall, would provide definitive evidence that the bursts are Galactic. Further limits on any angular anisotropy will constrain, and might rule out, the Galactic hypothesis. However, the limits that BATSE will be able to achieve are not likely to be definitive, since the angular distribution of bursts from the distant Galactic corona can be very isotropic.
Detection of a concentration of bursts toward Andromeda, either by
BATSE, by lengthy (> 20 days) X-ray (2-10 keV) observations using
imaging X-ray telescopes (Yoshida, Ogasaka, and Murakami 1994), or a
scintillation counter experiment with 
times the BATSE
sensitivity would provide definitive evidence in favor of the Galactic
hypothesis. However, the absence of any concentration toward Andromeda
could not be taken by itself as definitive evidence against the
Galactic hypothesis, since the bursts might well be beamed along the
direction of motion of the neutron stars (Li, Duncan, and Thompson
1994). Then only the rare neutron star whose motion is almost directly
toward us would be visible to BATSE. The few resulting bursts from
Andromeda would always be swamped by bursts from the many high velocity
neutron stars born in the Milky Way and moving away from us.
Cyclotron lines. Other spectroscopy instruments will soon be flown (e.g., TGRS on Wind, Konus on Wind, HETE, Konus on Spectrum X-Gamma, etc.) which will search for lines. Further confirmation of the existence of cyclotron lines would provide strong evidence in favor of the Galactic hypothesis.
Repeating. The new bursts in the third BATSE catalog are not expected to suffer from the same limitations which afflicted bursts in the second year of observations due to failure of the tape recorders on-board tape recorders. It is therefore expected that the third BATSE catalogue will provide a fair test of repeating hypothesis.
Counterparts. If quiescent counterparts were found, they would likely provide the most immediate and powerful information about the distance scale to gamma-ray bursts. But the chance of finding counterparts is unclear, particularly if the bursts come from distant high velocity neutron stars in the Galactic corona. The BATSE GROCSE network is providing approximate positions of bursts in real-time for ground-based searches. HETE will provide more accurate (few arcsecond to few arcminute) positions in real-time for ground-based searches. Missions have been proposed (e.g., BASIS and ETA) which would produce 1" burst positions; these missions would definitively answer the question of repeating and determine whether or not the bursts have visible counterparts at other wavelengths.
Serendipitous discovery. The discovery of gamma-ray bursts was serendipitous and many of the most important advances in the field have come from unexpected discoveries. Thus, if history is any guide, the distance scale to gamma-ray bursts will most likely be established through some entirely unexpected or serendipitous discovery.