A handful of things to take away (not exhaustive by any means)…
(1) First, there’s a lot more to come from Planck. Of note, the polarization data isn’t out yet, and this is one place where Planck will shine. (A range of cosmological phenomena imprint their signatures on the polarization of the CMB photons.) But for now…
(2) There are two spins you can take on the overall picture. Spin 1: The Planck data has demonstrated over an impressively large range of angular scales that our standard picture of cosmology works. It’s a shining example of a reasonably elegant set of theoretical predictions for a rather complicated system (the friggin’ universe) showing excellent agreement with precision data. Spin 2: It’s a rather boring suite of results because everything just agrees with what we already thought, only now we have more precision on the underlying parameters in the theory.
(3) On to more specific things… As discussed in the inflation thread, Planck’s sensitivity to the smallest angular scales has allowed a fairly strong statement that the power spectrum is not scale-invariant, a prediction of most models of inflation. This adds significant weight to the inflationary picture.
(4) Number of (light) neutrinos: A feature of previous data was a preference for too many “effective relativistic degrees of freedom”, a jargon-y but more precise way of saying “number of very light particles”. The expected number is 3.046, a non-integer since heavier particles do contribute ever-so-slightly to the same observable features as the very light particles. Further, the “3” part comes from neutrinos, which come in three varieties.
Right… so earlier data suggested this number N[sub]eff[/sub] was around 4, but with large enough error bars not to get anyone too excited. The reason there has been some excitement, though, is that there is a suite of unexplained anomalies in particle physics experiments that could be happily explained if there were a fourth neutrino.
The new Planck data gives N[sub]eff[/sub] = 3.30 +/- 0.27, in good agreement with the simple expectation of 3.046 and in rather poor agreement with 4-ish. The basic interpretation of this is: no, guys, there really are three neutrinos.
(However, a technical aside for those interested: something that I haven’t seen mentioned in any summaries is the following. A new neutrino would have to be sterile, that is not directly experiencing the weak interaction. Thus, a sterile neutrino only contributes to N[sub]eff[/sub] if it has significant mixing with active neutrino flavors. In general, the perturbation to N[sub]eff[/sub] from a sterile neutrino could be arbitrarily small. Of course, there are lower limits on the mixing provided by particle physics data, so one can attempt to rule out those sterile models (and I suspect such papers will appear imminently on the arxiv). )
(5) No evidence for “non-Gaussianity”. Many exciting universe origin stories predict that the CMB fluctuations would deviate from idealized Gaussian behavior. Planck’s new precision searches for non-Gaussianity have come up empty.
(6) No evidence for novel structure, cosmic strings. The early universe had a lot of energy kicking around, so physical phenomena that only manifest themselves at high energy can take place in the early universe and (hopefully) leave a fingerprint. Planck’s searches for such fingerprints have also come up empty, culling some grand unified theories from the herd.
(7) Cosmological parameters better measured. As you note, the cosmological parameters are all nudged around a bit, but nothing moved more than allowed by the previous or new measurement uncertainties.
(8) Limit of the sum of the neutrino masses. The CMB allows a measure of the sum of the neutrino masses. Planck has provided an upper limit (which is all we have ever had) and the result isn’t earth-shattering, although it is of note that higher masses are allowed when they could have been strongly ruled out. (A large value for the sum of the neutrino masses has positive ramifications for a suite of other experimental measurements.)
(9) Low-multipole anomalies. A lot of the headlines have focused on unexplained anomalies at large angular scales. These anomalies aren’t new and are the same ones measured by previous instruments. They represent a real question in cosmology, but they aren’t what Planck brings to the table. However, if you want to write an article about the new Planck results, you have to talk about something.