We present an analysis of ~3.5 deg² of submillimeter continuum and extinction data of the Perseus molecular cloud. We identify 58 clumps in the submillimeter map, and we identify 39 structures ("cores") and 11 associations of structures ("super cores") in the extinction map. The cumulative mass distributions of the submillimeter clumps and extinction cores have steep slopes (α ~ 2 and 1.5-2, respectively), steeper than the Salpeter initial mass function (IMF; α = 1.35), while the distribution of extinction super cores has a shallow slope (α ~ 1). Most of the submillimeter clumps are well fit by stable Bonnor-Ebert spheres with 10 K < T < 19 K and 5.5 <(P_ext/k) < 6.0. The clumps are found only in the highest column density regions (A_V > 5-7 mag), although Bonnor-Ebert models suggest that we should have been able to detect them at lower column densities if they exist. These observations provide a stronger case for an extinction threshold than that found in analysis of less sensitive observations of the Ophiuchus molecular cloud (Johnstone et al.). The relationship between submillimeter clumps and their parent extinction core has been analyzed. The submillimeter clumps tend to lie offset from the larger extinction peaks, suggesting that the clumps formed via an external triggering event, consistent with previous observations.