I'm working with an ADXL335 (https://www.electro-tech-online.com/custompdfs/2009/12/ADXL335.pdf) - it's a QFN package and I see there are a few pins all labelled as "common". Will it be alright if I just use one of the common pins for my circuitry, or should spread my connections around and use as many as possible? What's the difference?
Similarly, can i just use one of the supply voltage pins (I see they have two labelled "Vs")?
Common pins are most usually connected together, it is sometimes for the IC stability since there are issues like internal capacitance, etc. Better connect them together.
Typically you must connect all supply pins to their appropriate levels. You have no idea how the bond wires attach to the die internally or even the structure of the die at that. Always connect everything when it comes to power and ground terminals.