What was done
The authors investigate climate-related processes that cause variations in global mean sea level on interannual to decadal time scales, focusing on thermal expansion of the oceans and continental water mass balance.

What was learned
The rate of steric (thermal-induced) sea level rise over the past 40 years is estimated by the authors to be 0.5 mm/yr.  From early 1993 to the end of the 20th century, however, analyses of Topex-Poseidon altimetry data and the global ocean temperature data of Levitus et al. (2000) yield nearly identical rates of rise that are approximately six times greater than the mean four-decade rate.

What it means
"These observations," in the words of the authors, "may suggest that an acceleration took place in the recent past, likely related to warming of the world ocean."  However, as they alternatively note, "the recent rise may just correspond to the rising branch of a decadal oscillation."  In addition, they say that "satellite altimetry and in situ temperature data have their own uncertainties and it is still difficult to affirm with certainty that sea level rise is indeed accelerating."  In fact, they cite the work of Nerem and Mitchum (2001) as indicating that "about 20 years of satellite altimetry data would be necessary to detect, with these data alone, any acceleration in sea level rise."

The bottom line is this: although one cannot deny that the rate of rise of global mean sea level appears to have strongly accelerated during the 1990s, proof of that proposition cannot be honestly claimed without another decade of similar-trending data.

References
Levitus, S., Antonov, J.I., Boyer, T.P. and Stephens, C.  2000.  Warming of the world ocean.  Science 287: 2225-2229.

Nerem, R.S. and Mitchum, G.T.  2001.  Sea level change. In: Fu, L.L. and Cazenave, A. Eds. Satellite Altimetry and Earth Sciences: A Handbook of Techniques and Applications.  Academic Press, San Diego, CA, pp. 329-349.