Out of curiosity, I have the same problem with mine. Where on the left side are you seeing the hinge though? I've had mine for a while and it clicks pretty loud; my best friend and brother have relatively new ones; best friend had for about a month, brother had for a touch over a year, both are great still. Mine also wobbles, but it's not too bad... pretty much just because it's... a hinged screen?
At some point I'm sure you'll see places like dealextreme and tmart carrying replacement 3DS cases.
DX sells the hinge axle.
http://dx.com/p/repair-parts-replacement-genuine-nintendo-3ds-spindle-module-128541
However it looks to be identical to the DSi one, save for the collar being (possibly) removable on it, but it's half the price.
http://dx.com/p/repair-parts-replacement-flip-open-screen-shaft-for-ndsi-dsi-24846
Except if these are anything like the DS Lite, it's not the axle, it's the shell. Which... yeah.