@StevenZ
Hello:
Apologizes for the late reply I just saw this, as you seem to be experiencing the same play back issues with the same tracks. I can suggest maybe a couple of things.
The first thing to rule out issues with the Spotify apps and the devices try doing a clean reinstall of the Spotify apps. A FAQ on how to reinstall the Spotify apps on your devices: https://support.spotify.com/learn-more/faq/#!/article/reinstallation-of-spotify/?in=search
Then once any issues with the apps is ruled out with a clean reinstall, try first the webplayer here: https://play.spotify.com/ double check to see if the songs play there or not?
If all three play locations, your phone, PC, and Webplayer fail. Try switching your phone off from your local network WiFi connection, and go through your phone provider as an access to the Spotify service, does content play this way? Note you need to be premium to play any content you want too, otherwise you might be stuck in a shuffle mode as an ad support mobile user of the Spotify service. If content plays fine through your phone provider, but does not play very well using your local network WiFi connection, you might be having either ISP connection issues, or your network router might have some features either disabled like UDP connections? Then a much more trouble shooting will need to be done to try and isolate the connection issue to the Spotify service. Any forum boards posting bad reviews of your ISP in your area is a good idea to check out as well? Any known issues with your ISP cutting bandwidth use by subscribers who use too much bandwidth streaming music and movies, spotty ISP services can cause odd things with some songs playing fine other songs getting skipped with ISP connections connecting and disconnecting often?
You can also do this to rule out maybe a direct account issue you might be having. If you have a friend who has a Spotify account, have him or her connect to their Spotify account using your PC and the Spotify app, and see if they have any playback issues with those same songs?
Post back with what you have tried, there is always a way for a fix. The Rock Stars here as a last resort can escalate issues and have a Spotify mod take a peek behind your account to check for anything causing problems.