I'm going to pull the dash to change out my heater core, but I'm sure I'll run into a lot of plastic clips/retainers. Is there a special tool to take them out more easily?

 

Removing the dash is one of the most difficult things I have ever done on a Honda. It's not an easy task, but I don't think you need any special tools. The main PITA for me was disconnecting all the various wiring harnesses. There are some DIY articles out there, so I suggest you follow them.
Official Dash Removal How-To *pics* - Team Integra Forums - Team Integra

 

Thanks for the link. And I actually did find a tool for the plastic retainers. You use it instead of a small flat head to pull the clips out easier/without breaking them.

 

I'd just replace the clips with new ones. The old ones are 15+ years old at this point and get brittle, loosen, etc. over time. You'll end up with less rattles just replacing them.

 

^ This. I replaced almost every damaged clip/ziptie. I didn't want the wires rattling. For the clips I could get out, I used needle nose pliers.
Good luck!