I seem to remember là from an early attempt to learn Gaelic. Later I learned latha. I had a look in my friend Am Faclair Beag, and almost all of the examples using là are for some kind of special day, a saint's day, birthday etc etc. Là na Nollaig, Là na Caisge. Would it be fair to say that this sort of situation là rather than latha would be the preferred form, then latha would be used in more "mundane" situations?
Ok, is this during listening exercises? Là is listed as an acceptable translation here, but not as an interchangeable homophone when "latha" is heard. This is on our list of things to change in the course expansion, but unfortunately it has to be done as part of a wider change. Tapadh leat a-rithist!