A lot of players are having trouble with completing their Daily Mission in the new Call of Duty: Modern Warfare, where they do progress towards the Mission, but this progress is not tracked later when they check.
Luckily for us, there is an easy fix for this problem. All you need to do is to restart the game. Completely close it, then boot it up again, and the progression should show up. The bug is just a visual bug, so you actually get progress towards the Mission all along, but it just won't show until you have reloaded your game.
If you play on consoles, make sure that you actually close the game and don't just minimize it. On the PS4 this is done by first going out to the main menu, then clicking on the Options button and choose "Close application".
Unfortunately this means that some users will have to update the game (if a new patch has been released since you began to play), which can take a while. So you should probably fix the visual bug at a point where you won't be too upset if you can't play for a little while. There's not a very big downside to waiting a bit with restarting your game anyway, since the progress is still tracked.