Viewing source in that manner isn't particularly more convenient than directly accessing the Spotify API JSONs, though.
The page as update can now submit directly to the server. After loading an album page from Spotify, you can load a Musicbrainz release by its MBID.
It will then check the track counts match (if they don't it simply does nothing)*. If they match, it then adds a final column with the retrieved track names (so you can check they are what they should be).
*It currently matches track counts in a very primitive way: it assumes there that the first medium in the release is the entirety of the Spotify release (which works for most releases, as long as additional media are DVDs etc.)
The other caveat is that the requests to the MB server are subject to rate limitting. If a request fails (as it often does), you can just try again in a few seconds/minutes. At the moment the page doesn't provide information as to why it hasn't matched a MB release (whether it was a problem with the ID, the server, or the track count didn't match).