  Using a mass-limited sample of 24um-detected, star-forming galaxies at
0.5<z<1.3, we study the mass-star formation rate (SFR) correlation and its
tightness. The correlation is well defined (sigma=0.28dex) for disk galaxies
(n_sersic<1.5), while more bulge-dominated objects often have lower specific
SFRs. For disk galaxies, a much tighter correlation (sigma=0.19dex) is obtained
if the rest-frame H-band luminosity is used instead of stellar mass derived
from multicolor photometry. The specific SFR (sSFR) correlates strongly with
rest-frame optical colors (hence luminosity-weighted stellar age) and also with
clumpiness (which likely reflects the molecular gas fraction). This implies
that most of the observed scatter is real, despite its low level, and not
dominated by random measurement errors. After correcting for these differential
effects a remarkably small dispersion remains (sigma=0.14dex), suggesting that
measurement errors in mass or SFR are ~0.10dex, excluding systematic
uncertainties. Measurement errors in stellar masses, the thickening of the
correlation due to real sSFR variations, and varying completeness with stellar
mass, can spuriously bias the derived slope to lower values due to the finite
range over which observables (mass and SFR) are available. When accounting for
these effects, the intrinsic slope for the main sequence for disk galaxies gets
closer to unity.
