The possible presence of dust in the broad-line regions of active galactic nuclei (AGNs) has been a subject of debate for years. On the one hand, the fragility of dust grains in the presence of an intense source of hard radiation, such as exists in the nuclei of active galaxies, argues against the survival of dust in the broad-line region (BLR). On the other hand, some AGNs showing large, broad emission-line Balmer decrements but more normal narrow-line Balmer decrements provide evidence for dust survival on scales of tens of parsecs. The Seyfert 1.8 and 1.9 galaxies are two classes of AGNs showing such characteristics. Arguably the most powerful method of detecting the presence of dust in the BLR is the predictable, time-variable effect on the flux ratios of the broad emission lines as dust clouds moving at high velocity pass across our line of sight to the nucleus. The line fluxes should change in a completely predictable manner with one free parameter, the extinction A(V), or alternatively the reddening, E(B-V). Several Seyfert 1.8 and 1.9 galaxies are known to show line flux changes of just such character, and on timescales of a couple of years which implies tangential velocities of hundreds to thousands of km s(-1). I present the most complete spectral survey of known Seyfert 1.8 and 1.9 galaxies to date and compare the spectra with previous spectra to search for changes in the broad Balmer emission lines. Nine of the 24 galaxies showed significant spectral variability. Confirming previous work on a smaller sample, I find that NGC 7603 = Mrk 533, Mrk 993, and Mrk 1018 show variability consistent with changes in reddening to the BLR. NGC 7603 in particular has brightened substantially in the past few years. Data on Mrk 915 are sparser, but this object, too, may be showing signs of changing extinction. NGC 2622 = Mrk 1218, another Seyfert which showed variability consistent with reddening changes, has declined in brightness over the past few years, and done so in a manner inconsistent with a simple change in reddening. Spectropolarimetry shows that this; object is complicated, however, with multiple paths for photons from the nucleus to reach our line of sight, ruling out any simple model. Two other Seyferts, Mrk 883 and UGC 7064, show variability in broad-line fluxes inconsistent with reddening changes, and their variability is probably due to real changes in the ionizing flux in the BLR. Both objects show no apparent change in their optical, nonthermal continuum fluxes. Analysis of some weak correlations found in the properties of the Seyfert 1.8 and 1.9 galaxies shows that those objects thought to have large Balmer decrements due to low optical depth and low ionization parameters in their BLR clouds have systematically lower H alpha(b)/H alpha(n) ratios and higher [O III] luminosities than those objects known to be affected by reddening. The senses of both of these weak correlations are opposite to what is predicted by the low-optical depth, low-ionization parameter explanation for these objects.