Hey Erin,
Oh shoot, so sorry for the trouble here!
Errors like this usually mean that there is a permissions issue on the server. In other words, WordPress does not have the correct permissions to move, delete and copy files in the server on your behalf.
To get around that issue, you could manually update the plugins on the server. That would mean downloading the Events Calendar PRO and Filter Bar updates here on this site (which you can do by logging into your account and heading to My Account > Downloads) and then following the steps outlined in this post to remove the old versions and replace them with the new versions.
Does this make sense and will it work for you? Please let me know.
Cheers,
Geoff