Some days I go out to start up my RX8 and after it warms up and I am ready to start moving there is a little resistance. The first time this happened I was confused and thought I had hit something, but my car was unscathed. However this has happened multiple times in different temperatures cold and warm. When backing out there is a little resistance as if I left my parking break up, and then a pop and I can move again. Any idea what this could be?

 

Was it sitting for a long time? Is it auto or stick? Could just have been the brakes were stuck and "popped" back to normal.

 

Sitting overnight, not very long. Manual 6SPD. Sometimes it makes a kind of whiny noise in reverse as well...

 

Was it rainy or damp? Most likely it was just the brakes sticking(you should inspect them) and almost every car "whines" in reverse because of the direct cut gears that are used for reverse.

 

Yah, I've had my car make fun popping or clanking noises when I first set off a few times. It only happens when I use the handbrake and only when it's wet or humid out so I'm pretty sure it's the rear pads sticking to the rotors due to rust.

 

Good to know! It's been pretty humid/wet most times. At first it was icy and I assumed there was a chunk of ice in my wheel or something.

 

Could just be the abs, sounds like what's in this tsb:
https://www.miata.net/garage/tsb/sb04_002_14.pdf