I haven't had any Internet issues generally on the 3DS thus far, but when trying to connect to someone who has opened their gate, after a brief delay, I get an error code 006-0502 that I cannot connect to partner's device. Any ideas?
006-0502 means that the connection was broken at some point during the process. Since you haven't had any Internet issues before on your 3DS, maybe the problem is on the other person's end? Do you have the same problem when trying to connect to a different person's town?
There's no place like 192.168.0.0/16.