Per the Google Drive Help page:
We've received reports of users seeing comment indicators on cells in which no comments exist, as well as comment indicators in the incorrect cell after a sheet is resorted, duplicated, or amended by copy/paste.
Our team is aware of the issue and working on a fix. As a workaround, if you notice out-of-place comment indicators, simply refresh the spreadsheet. All comment indicators should appear in the correct cells again.
Following these instructions, I tried simply hitting the refresh button and all of the phantom comments disappeared. I guess sometimes the easiest solution is the best one.