http://www.sdss3.org/dr8/spectro/catalogs.php
Each object has a classification (CLASS) and a redshift determination (Z) with an associated error (Z_ERR). For galaxies, a velocity dispersion can be determined (down to about 70 km/s). The redshifts are determined by fitting models to each spectrum assuming a large range of possible redshifts. The best model is chosen on the basis of the chi-squared value of the data with respect to the model.
In addition, there is a bitmask called ZWARNING which has flags set in suspicious cases. A ZWARNING equal to zero indicates no problems identified. Most bits in that mask are signs of substantial problems; the exception is the MANY_OUTLIERS bit, which can be set for successful spectra that either happen to be very high signal-to-noise ratio (e.g. bright stars) or unusual (e.g. some broad-line AGN in galaxies).
The classifications are stored in the CLASS and SUBCLASS parameters. They can take the following values:
STARFORMING: set based on whether the galaxy has detectable emission lines that are consistent with star-formation according to the criteria:
log10(OIII/Hbeta) > 0.7 - 1.2 * (log10(NII/Halpha) + 0.4)
AGN: set based on whether the galaxy has detectable emission lines that are consistent with being a Seyfert or LINER:
log10(OIII/Hbeta) < 0.7 - 1.2 * (log10(NII/Halpha) + 0.4)
If any galaxies or quasars have lines detected at the 10-sigma level with sigmas > 200 km/sec at the 5-sigma level, the indication "BROADLINE" is appended to their subclass.
As examples, the full resolution version of the figure showing the spectra on the spectrum page lists the CLASSes, SUBCLASSes and error flags of these particular spectra.
For each object, there are also detailed quality determinations, a full description of the templates used, and the targeting information. See the CAS table schema or the the specObj file datamodel page for full information.