Not much to say. This has been an issue for years. The web player in Chrome and IE is skipping songs. It goes from song to song without playing them.
Hey @PhineasFinn! Welcome to the Spotify Community. ^^
I'm sorry to hear this.
Is your web player still not able to play music properly? If yes, could you try to clear your browser cache/cookie to see if that makes any difference?
Let me know if that helps, thanks! ^^