Unbelievably high masses/ densities in NASA website data In May, I did my own amateur analysis of Kepler data that was supplied here. This was a table of all confirmed "Kepler planets" to date (April 1, 2015). This table had some unbelievably high masses/densities listed in the first column after the planet designation (ie: planets of Kepler- 23, -24, -25, -27, -28, -32, -39, -48, -52, -54, -57, -58, -59, -60 and others). I didn't take these seriously, but would like to know if there was a "units" error or something I am missing. To give you an idea, Kepler-23b is given a radius of $1.9 R_{\text{Earth}}$ and a mass of $254.3 M_{\text{Earth}}$ - and that's nothing compared to some others. I checked just now and the data is the same.
Starting from the index you mentioned, I clicked through the links for some individual planets, which in turn link to discovery papers or other relevant observations. For planets around Kepler-23, -24, -25, -26, -27, and -28, the relevant papers are Ford et al. (2012) and Steffen et al. (2012), two out of a series of papers. Both papers used transit timing variations (TTV) and something called dynamical stability, which gives an upper limit to the mass of the planets such that the relevant n-body system is stable over long timescales. This leads to plots like the following (Fig. 3, Ford et al.):



The arrows indicate simulations where the system was stable over timescales greater than $\sim10^7$ years.

Additionally, as Ford et al. note,


  We caution that the uncertainty in the masses and sizes of the host stars directly translates into uncertainties in the planet masses and sizes.


Furthermore, shorter observations by Kepler also lead to larger uncertainties. Thus, the maximum masses of the planets as given in these simulations may very well be much greater than their actual masses. Steffen et al. have similar results, and they use a very similar method.

After more reading, it's clear that the same is true for planets around Kepler-32, Kepler-48, Kepler-52, Kepler-54, and Kepler -57 to -60, inclusive.

Kepler-39b is interesting. The paper NASA cites, Bouchy et al. (2011), states that the object is larger than one would expect, even taking into account that there is a large uncertainty in radius. It may be a fast rotator (see Zhu et al. (2014)), which would explain its oblateness, but that still isn't enough to explain the discrepancy.

Now, I referred to Kepler-39b as an "object", not a planet. NASA lists its mass as over 20 Jupiter masses; Bouchy et al. placed it at about 18 Jupiter masses, with a very low uncertainty. This could mean that it's more like a brown dwarf than a massive gas giant, and remember, the distinction is fuzzy when it comes to sub-brown dwarfs. This, then, may be the most likely explanation.