Jim gave a great review of the equation of state of dense matter, and what can be (and has been) learned from neutron star observations.
The room was very interested in PSR J1903, which was reported discovered by Champion et al (2008). Jim mentioned more recent observations by Freire, in which with 95% confidence limits the mass to be above 1.65 solar masses.
Jim also mentioned that, from chiral EFT, Hebeler and Schwenk (2009) determine that a 1.4 solar mass star will have a radius of 11.5 +/1.5 km.
The distance to the INS RXS J1856 has been a long standing question, since this affects the interpretation of observations of its thermal spectrum. In an updated work, Walter Eisenbeiss, Kim and Lattimer (2010) find a distance to the isolated neutron star 1RXS J1856 of 115 +/- 8 pc with 2002-2004 HST data. They conclude that the results in conference proceedings (van Kerkwijk & Kaplan 2007) find D=167 +/- 16 pc must be flawed.
Jim also presented a Bayesian analyses performed by Steiner, Lattimer and Brown (2010), using existing constraints on measurements of neutron star masses, radii and redshifts (qLMXBs M13, Omega Cen, and 47 Tuc X7; INS RXS j1856; and constraings on EXO 1745-248, 4U 182-30, and 4U 1608-522), and this places interesting constraints on the nuclear properties of the equation of state (such as the symmetry energy; the compressibility, for example, is constrained as well as it is with nuclear experiments. A factor of 10 increase on the number of such objects observed would surpass nuclear constraints on these equations. The group was particulary interested on the joing constraings due to 47 Tuc X7 and M13, since those qLMXBs are extremely disparate in their radiation radii.