Removing the cover art is easier than correcting it, but I'll cover a few options.
Removing all album art from Google Play: From the songs page, select every track. Right-click within the selection and select 'Edit Info' from the pop-up menu. On the cover art icon, click the X to delete the cover art from all your songs.
Removing just the bad album art: Create a playlist for albums with bad cover art. Go to the Albums page and add the ones with bad art to the new playlist. Select all the songs in that playlist and delete the cover art as above.
Actually solve the problem: First, you need to edit the ID3 tags on your MP3s. (I'd be surprised if these were not the source of your album art troubles. Edit: Looks like I was completely wrong about that. Seems Google Play has some album art problems and they know it. Mea culpa.)
If you have Windows, download Album Art Downloader from SourceForge at http://sourceforge.net/projects/album-art/. HowToGeek has a nice step by step process for correcting your MP3 library's album art.
If you are on OS X or Linux, it is a bit trickier because there is not one standout bit of software that I've used to fetch and embed album art. iTunes, for example, does not automatically embed album art in your ID3 tags and the process for doing so depends on what version of iTunes you are using. Blegh. However, the song metadata at MusicBrainz is pretty good and they have a cross-platform-ish ID3 editor called MusicBrainz Picard that, with a plug-in called Cover Art Downloader, will grab covers for all your albums and embed them as needed.
You still need to delete cover art in Google Play to get the new art to update. In fact, you may need to delete entire tracks or albums and re-upload them with the new ID3 tags. In researching this I found the latter method to be effective and sufficiently quick, but your mileage may vary.
Best Answer
First: did you also remove the song from Google Music recycle bin, after deleting it from your library?
There is a chance that if you upload a song that Google Music is recognizing as the same as the one you deleted, it will restores it from recycle bin, if it's still in there.
I don't know if you know already but this is how Google Music works:
when you try to upload a song it will try to "Scan and Match" it to its catalogue of songs by comparing the waveforms (sort-of).
if there is a match it will not let you upload the song, but it will add a high quality (320 kbps) version of that song to your library (for streaming only: later on if you try to download that song to your computer it will send you a version with the closest bitrate to the one you tried uploading).
if there is no match then your file will be uploaded and retain the quality it has been encoded at (obviously)
So I guess what was happening in your case was that when you were uploading the tone-clean song, either Google was restoring the song from its recycle bin or, in case your removed it from the bin as well, Google Music was probably still matching the tone-cleaned song with the original song (containing disturbing tone) from their catalogue and adding that to your library again.
Also, this answer to a similar question can also be useful in understanding what was going on.
I don't know how exactly you managed to upload the tone-corrected song with Firefox, but I am quite confident that the reason it worked had more to do with a mix of the factors I explained above than with something else.
I hope it helps, if not for this case, maybe for future ones.