Playing the first mission I could never get it to advance past the landing at Tskhinvali. After a few attempts to make sure I wasn't doing something wrong, I opened the mission in the editor to check the trigger conditions.
The problem appears to be with the altitude condition, which is currently set to "lower than 905m". The problem is that there are two 4-pad FARP objects at Tskhinvali, but the northernmost one is slightly higher up than the other. The trigger's <905m condition is only satisfied if you land at the lower FARP (PosTshinval2), while the upper one (PosTshinval1) is slightly too high for the trigger to activate. Its altitude condition needs to be raised by a few meters.
Also, due to what I assume is the usage of two FARP objects, there are two entries in the ATC radio menu. This doesn't seem to interfere with the mission, but it is somewhat confusing having multiple "Shpora" entries in the menu.
EDIT: I use imperial units in my F2 view, but converted into meters the landed altitude at the upper FARP is 906m while the lower's is 904m. So the altitude condition for PosTshinval1 should probably be raised to 907m or so.