I have encountered two separate problems, but I am putting them in the same question in case they are related.
First, my Trash would not empty. It seems to be getting stuck on certain files, because I will reset my Macbook and some of the files will be deleted, and then if I remove a file or two at random, more can be deleted. Some of these files had strange characters in their names. I tried changing the names to single characters, but this did not help.
Next, I attempted to backup my Macbook using Time Machine. I plugged in the HDD I've been using for this, but every time I try to start the backup, Time Machine gets stuck at "Preparing to Back Up".
I definitely need to know how to fix the Time Machine problem, but I am curious how to solve the trash problem as well, and whether or not these problems are related.
EDIT: Console.app logged the following this morning before I left on a trip. I did not bring the HDD with me.
6/5/12 7:41:28.312 AM com.apple.backupd: Starting standard backup 6/5/12 7:41:46.877 AM com.apple.backupd: Error -35 while resolving alias to backup target 6/5/12 7:41:58.368 AM com.apple.backupd: Backup failed with error: 19 6/5/12 7:59:08.999 AM com.apple.backupd: Starting standard backup 6/5/12 7:59:10.187 AM com.apple.backupd: Backing up to: /Volumes/Seagate 3TB Mac/Backups.backupdb 6/5/12 7:59:13.308 AM com.apple.backupd: Event store UUIDs don't match for volume: Macintosh HD 6/5/12 7:59:13.331 AM com.apple.backupd: Event store UUIDs don't match for volume: Blank 6/5/12 7:59:13.683 AM com.apple.backupd: Deep event scan at path:/ reason:must scan subdirs|new event db| 6/5/12 8:23:31.807 AM com.apple.backupd: Backup canceled. 6/5/12 8:23:33.373 AM com.apple.backupd: Stopping backup to allow backup destination disk to be unmounted or ejected. 6/5/12 9:51:21.572 PM com.apple.backupd: Starting standard backup 6/5/12 9:51:22.515 PM com.apple.backupd: Error -35 while resolving alias to backup target 6/5/12 9:51:32.741 PM com.apple.backupd: Backup failed with error: 19