I try to keep my acceptance rate at above 90%. Is there a way to filter for questions that have not been accepted so I don't have to check every one? Seems silly but as the number of questions grows the task gets harder.
Currently, I know of no way to filter out questions with an accepted answer. The fastest way is to look for the green rectangles around the number of answers:
The posts with the green rectangles have an accepted answer. (I'm sorry if you already know this, it's the only way I know to look for questions with(out) accepted answers other than opening them).
The answer by Martin Sleziak seems to answer your question in the affirmative. This link should show you what you want.
If you have a look at help for advanced search you will find out that hasaccepted:1 returns questions which have an accepted answer and hasaccepted:0 retuns questions which do not have an accepted answer.
You might want to sort the search results according to your preference (newest/active).
To find your own questions without an accepted answer you can search for hasaccepted:0 user:me. (And again, you can then sort the results in the way which is suitable for you.)