Is a leak in my sink drain caused by a connection that's too high?
First thing to consider is that that connection will always be filled with water, because it's presumably the low side of the trap (hard to tell for sure from the photo, but it should be).  So, that connection needs to have extra attention; it needs to be tight, but before being tight, it needs to be perfectly aligned.

One reason it needs to be perfectly aligned is because (I believe) there is often no washer at that connection. My experience is only with PVC drains, but with them, that section of pipe from the waste side is tapered at the end rather than straight, and should not have a tapered washer like all other connections.  The pipe itself will be shaped like the washers if this is the case. I think there are a number of different configurations here, so it may require no washer, or a different type of washer, or maybe a standard compression washer.  

The extension piece seems to be necessary to align to the waste connection at the wall.  If properly connected, there should not be a problem with leaks.  It looks like a normal connection.