What are the pros and cons of wingtip tanks?
I happen to own a homebuilt with tip tanks for ALL of the fuel supply (Pazmany PL-2), and while they look really cool, I'd prefer the fuel was in the wing leading edges mid span.


There is no aerodynamic benefit.  The tuna fish shaped tank doesn't function like a winglet (it has to be a wing to work like a winglet) and is too small to have any kind of end plate effect of significance (an end plate has to extend for a full chord to do any good that exceeds its own drag).  The flattened and canted tanks you see on twin engine Cessnas was intended to produce a bit of vertical lift and an enhanced dihedral effect to offset some of the inertial issues in roll that the fuel mass creates; which leads to...
Inertial issues in roll.  The mass of the fuel way outboard in the wings is a total pain.  It deadens the aileron response.  The inertia magnifies roll and yaw disturbances. My airplane is much more snappy with minimum fuel vs full fuel, and wags its tail in turbulence much less. I prefer to fly it with about 1/2 fuel if I'm just going out for an hour or so.  The  mass also kills a lot of the roll-yaw couple and amplifies adverse yaw.  If I skid the airplane with rudder, the roll into the yaw is very mild, in spite of significant dihedral.
Significant form drag. On my plane there is about a 8kt speed penalty from having the tanks taking up space in the airstream (based on the performance of other PL-2s modified to tankless wet-wing).
Fuel imbalances have a huge impact because the arm is so long.  If I ran one tank all the way down with the other nearly full, I'm sure it would use up an unpleasant amount of my aileron authority at low speed (I don't really want to find out how bad - at minimum, it would take probably 10lbs plus of side pressure on the stick to keep wings level). Having no trim tab or bungee, I use the fuel balance as my lateral trim, and when solo, have to achieve about a 2-3 gal right side differential to get the plane to fly hands off.  Then I have to remember to switch back and forth every 10 minutes or so to keep the balance.  I know if I forget because the airplane starts to wander off toward the heavy side, like a horse that suddenly remembers where the barn is while you're riding it.
Structural issues are minor.  You are adding mass at the opposite end of the most highly stressed part of the wing, but you need to make the outer spar structure able to handle the local bending, so some minor reinforcement would be required at the attachment.
One plus is the fuel supply is far away from you, say if you flipped over.  I like that.
One minus is the fuel supply is far away from you, at the first point to touch the ground in any kind of landing excitement.


All that being said, the PL-2 is a delightful airplane even with the tip tanks, and dammit they look awesome.  If I was building one from scratch however, I would do leading edge tanks like the Van's RVs.  Just way more efficient in every way.  As a long range fuel supply add-on however, they can make sense, but I think most designers will just extend the wet wing volume instead, until they run out of that.

On airplanes like the Lear, they made sense because with the super thin wings they were the most practical way to put in a large fuel supply.  But you will notice that they did away with them in later models because other than a handy place to stick tanks that don't get in the way of something else, it's mostly negatives. I shudder to think about how to control a tip-tank Lear with one side nearly empty and one side nearly full, if that were to happen somehow.  

A former colleague was an old F-101 Voodoo driver who also had a lot of time in T-33s and he recounted to me once that the T-33's really large tip tanks were a pain due to the flywheel effect of the fuel mass. A little bump would start it rolling, and with the big weights out there, it took more than the normal input to stop the roll and if the conditions were rough you were fighting that constantly.