Hi, thanks for your comment.
It's when I click '+' on a song, not when downloading a playlist. I was away from my Windows PC and listening to some new albums on my laptop, I pressed '+' on several songs (more than 10) and when I checked my phone I had them added to my library, then when I was next on my PC I clicked 'Songs' on the left-hand side and the song's didn't appear. I decided to check the web player and when logged in the songs appeared similarly to my laptop and phone. I think it's an issue with the Windows application not refreshing data properly. When I'm at home and press the '+' on my PC, I can check my phone and already can see the song appear and it begins downloading (same with my laptop).
Also, I noticed something that may not be easy to explain, but I'll try anyway. So, when you're listening to a song on the PC app, you can click the album art and it will take you to where you started playing the song from.
E.g., Say you were listening to a song from your Discover Weekly playlist and then changed the screen to anything else (whilst still playing the same song) to another playlist, an artists page etc, when you click the album art in the bottom left "currently playing" section, it will take you to the 'Discover Weekly' playlist and even scroll down (if needed) to exactly where you first clicked to play this song.
So, I went to the web player in Chrome and played a song that was not appearing in my Spotify desktop app, but WAS a song that I added earlier on and played the most recent one. If you're logged into the same app in multiple places you can choose where to play the music from and it'll tell you where it's being played; since I was playing it in the web app, the desktop app said it was being played there.
Then, I clicked the album art in the DESKTOP app and it went to my 'Songs' and highlighted the first song, it was the correct position of the song but since the Windows app had not synced properly it was highlighting a different song. I even waited a couple days and it didn't show up, trying to log out/in and it didn't work, I ended up uninstalling and reinstalling it and it then showed everything, it sucks though because uninstalling removes all of my downloaded songs and I'll have to re-download everything and if the bug comes back, I'll have to do it again...
This may be a bit confusing but if you try to follow my steps you should see what I mean. Let me know if you need clarification on anything and sorry for the long post!
Thanks.