The subject pretty much said it all. I have removed apps I don't use, clear the log once a week or whenever it starts running slow. I did a reboot with taking the battery out and it seemed to help some, but will it last? Clearing the log helped initially, but now I'm having to do it more often. How do I know I have the most current OS? Would that be causing it?
Whenever I hear BB 8330 running slow, as you have already suspected, I look at memory issues. Another area to look at is your browser cache. I empty mine every time I close the browser. I Clear History, Content Cache, & Pushed Content. I don't clear Cookie Cache as this is where your login for different sites is contained. You could always try a hybrid OS at BBTweaks.com. That may speed things up also. Read the article there on "How to Maximize Your BB Memory".