I just bought this bike yesterday -- my first ever bike.  I took it over to a friend's and he noted how my throttle feels loose.  Meaning, that there is about a 1/8th turn of "play" from when you begin to turn the throttle and when it catches with the chain.  Is this anything to be concerned about, and is there anything I can do to fix it?

Is there an actual difference in the tension between that 1/8th inch and the rest:
YES:  Take your tank  off and adjust the throttle cable at the carb, just back the screw housing out until you work the slack out and screw the locknut down.
NO: If tension is the same throughout it's not your cable.  Your Carb is jacked up and needs to be cleaned and/or rebuilt

It's the former scenario.  Nice to hear I just have to back the cable out to work out some slack.

Welcome!

There is also another adjuster closer to the handbar (8mm and 10mm open-end wrenches - can use carb wrenches (the little three inch ones for working on car carburetors).

I'm the friend who looked at the bike, I didn't even think to try the adjuster near the bar... was thinking of the one down by the carb. I'm a tard. It's a good lookin bike though!