It's difficult to define where to draw the line. Hopefully anyone who is a flying instructor would be mature enough to know what was appropriate.
I met my husband when he started learning to fly with me, but I resisted going out on a date until he had finished his PPL. (Such self control!) Now we're married we always seem to bring out the worst in each other when we fly together so it was a good thing we waited. I got another instructor to do his CPL training or it could have been a disaster!
On a more serious note, there are cases of harrassment sometimes, or what the student may deem as harrassment. I heard of one friend of mine, a gentle soul, who was very wrongly accused of sexual harrassment when he reached for the trim wheel in a tomahawk and accidentally touched her leg. On the other hand there are a fair few dirty old (and young) men out there who should never be in close proximity to a female in an aircraft.
The respect that students (should)feel for their instructors can make them vulnerable, and if alcohol comes into the picture major problems can develop very quickly. So I'd say, make friends, have a laugh, but instructor and student should keep a respectful distance at least until the training is complete, and if you can't keep your hands off each other change instructors!