Brake callipers not long enough to allow adjustment of pads I upgraded the standard Tektro brakes on my SE Lager to Shimano 105s. The braking performance is vastly improved. I also have Charge Plug wheels, rather than the stock wheels.

However I've noticed that there's not quite enough adjustment in the calipers to position the pads correctly. Even at the lowest position in the caliper arms, the pads are still very slightly too 'high' and overlap the upper curve of the rim.

Is this a problem? Is there anything I can do to solve it?
Those pads do look ever-so slightly too high on the rim, the main danger being that any slight vertical eccentricity could result in the pad contacting the tire and causing a blowout.

There are two main solutions:

Firstly, you could use a round file and simply file out the bottom of the slot slightly to increase the clearance.  This works best if you only need a very small amount of additional reach and are willing to accept permanently modifying your brakes.

Secondly, you could buy a set of brakes with a longer reach.  The Shimano 105mm calipers are 39-49mm reach; if you instead purchase some higher-quality dual pivot calipers that are 47-57mm reach you'd have plenty of room for adjustment and should be able to achieve equally good braking capability.