So, I have a 2007 350Z Stock. While driving home today, I noticed that while pressing in the clutch my RPM's would jump to around 2k-2.5k and wouldn't drop until I let out the clutch. Also seems the shifter jumps an 1/8" or so after letting off the gas pedal or while applying pressure to the gas pedal. Any thoughts?

Welcome to NICO!
Sounds like you might have a slight vacuum leak.
To check for vacuum leaks, get the car running and spraying carb cleaner around any and all vacuum hoses (one by one) and listen for the engine to rev up. If it does, spray again and isolate the area and potential hose. Replace it and see if a difference is made.

Test that out and let us know that you find!

Thanks for the reply! Will test it out when I get some free time!