I think the suggested improvement clarifies what he means: if you're worried that the UI element the user is interacting with doesn't fully convey what's happening, then improve that element rather than adding a second element that divides the user's attention and challenges them to read quickly and make the connection themselves. Communicate the failure of their interaction in the context of the element they interacted with, so the connection is clear.
A toast makes sense as a worst-case, last-gasp, no-context attempt to communicate with a user. In this example, if the user unchecked a playlist and dismissed the list of playlists while the save was happening, and then the save failed, a toast makes sense because the context of the action is gone. Might as well put the information at a random spot on the screen.
Even then, a toast probably isn't the best you can do, if you really want the user to understand the error. In a the-user-is-the-product adware application like YouTube, you probably don't care if the user misses errors like these (and might even prefer that they do), but in a business application you wouldn't want to gamble on the user missing the toast or confusing it with a different error. It might be more helpful for a normal user if you re-open the element and show them the error in context. Open up the list of playlists and animate something to draw their attention to the fact that their change didn't save. I'm probably getting pie in the sky here, because that sounds really difficult to do in a systematic way, but in an ideal world, you'd always see errors in context.