I am trying to select the loop of faces that you see partially lit all around the sphere. Please note that I am able to do that for all the other loops by clicking on alt+rmb. Whith these thinner sliceses (that i obtained by adding loop cuts). I have tried in any way also searched the web and videos, but wasn't able to find a way out. Any suggestions please?
This is an old question, but in case anyone else has this issue in the future:
Loop select with
alt+click will choose which loop to select based on which edge the cursor is closest to.
To select smaller slices, hover the cursor over the shorter edges of the faces when selecting.
you have two ways (each one is responsible in its case):
1- use loop selection*: Go to face-mode by pressing 3 (or vertex-mode by pressing 1); hold <Alt and click on one of perpendicular edges along the face-loop.
2- use shortest path: Go to face-mode by pressing 3 select one face. hold down Ctrl and select some other face and the shortest path would be selected. do this consecutively to select your desired faces.
You can also select these faces by going in side view (3 on numpad) then set she shading to wireframe with shift+z and then select the faces using box select (ctrl+b).
And also your issue may come from double vertices. To delete them you can use the "merge by distance" in 2.8+ and the "remove doubles" in 2.79-. you should then be able to select your face loops.