The user edition of Neon is based upon Ubuntu 16.04 LTS.
Does this mean that we wil have to cope with old mesa versions?

My laptop has Intel graphical hardware and I understand that it got much better in recent times.

Are there plans to switch to mesa 12.0.2 or so with Neon? And if not is there a way for me to get the latest stable mesa?

mesa is a part of base system,neon base is ubuntu 16.04.
so mesa version depends to ubuntu release.
maybe in 16.04.2 mesa and xorg components gets updates.
you can update mesa and xorg version manually with this ppa:

ppa:oibaf/graphics-drivers


its your own risk.maybe breaks your system.

Thank you for your reaction.
This is exactly what I mean: there is no way in between.
It's either the 11.2 (for now at least) or the 13 from oibaf.
At this moment there is not really way to get the version 12.03 is my sad conclusion.

I understand your point but for neon it is not wise to walk too far behind with mesa because these drivers are really important when using wayland and so. But for ubuntu updating mesa is not such a big priority because they are still using X with unity 7.
Anyway, let's hope they update mesa with the next point release.