Can I replace the mid 2012 motherboard on my Macbook Pro 15 in Retina with a more recent board (say 2015) without running into any compatibility issues?

No. For all the reasons @kaz-k mentioned. Once in a while it may be possible to do this between two models that are just a generation apart and otherwise share the same hardware with the only difference between Logic Boards being a CPU, but even then it is rare. About the only thing that usually works is installing a Logic Board for the exact same model year which has a faster CPU. For example if you had a Logic Board with an i7 CPU for the same exact model as your laptop, then you could install it to upgrade from an i5 CPU (same if using a Logic Board where the i5 CPU is 3.1 GHz instead of 2.5 Ghz....again assuming the Logic Board is made for that exact model.

I know the 2013 & 2014 models share a lot between them, but I don't even know whether their Logic Boards can be swapped between them. The 2015 model had a lot of hardware changes so the parts for the 2015 can only be used in a 2015 model (there may be some minor exceptions such as Speakers, but I don't believe any of the other major components are compatible with even a 2014 model).

Any legitimate part seller will clearly state which exact models any particular part is compatible. If the seller does not clearly state exact models, then I would not deal with that seller since those details are really important.

I should also mention that the 2012 Retina model I believe is its own unique model which is different enough to the 2013 Retina model. Of course the non-Retina model has nothing in common with the Retina models. Plus the 2012 non-Retina model is not even physically compatible with the 2011 model, even though they are very close (one of the mounting posts is off by about one mm, and the Displays are incompatible between 2011 & 2012).

Hi,

I think you can't, since ports location is different and mid 2012 logic board display chip can't handle retina screen.