Unfortunately, I'm getting better at drilling rivets out. It doesn't look too bad from this side, but I didn't take a photo of the shop-head so let's not focus on that shall we?
For the record, I thought I'd add a sequence of images showing the removal of a rivet set that didn't go quite according to plan.
1) For the simple reason I don't want to drill any section of the skin or structure of the plane, I need to make sure (as much as I can) that I'm drilling out only the rivet. That being the case, I find it best to start drilling in what you think is the centre of the rivet. For various reason (lighting; width of drill; angle of drill), sometimes I may not be able to know I'm not actually drilling in the centre of the rivet. Therefore, I drill for few short revolutions and check. Below is not quite in the middle but at this point it can be straightened.
2) Change the angle of the drill slightly so I'm drilling more towards the centre but being careful not to increase the angle too much or the drill bit may go skidding off down the skin.
3) Drill about 1-2mm into the rivet and break off the rim of the rivet head as below
4) At this stage, I would normally grab the other side of the rivet with a small pair of side-cutters and gently wiggle it free which works most of the time.
5) I can't recall why (at the time of writing this), but I've drilled right through the rivet which obviously makes it difficult to grab whatever's left. I'm assuming the shop head, was so damaged I couldn't get a grip on it which meant I was forced to push the remnants through with a punch.
Maybe there's a better way to do this, but I haven't seen it yet.