I have had the same thought. I would seriously worry about adding anything which might cause a snag. I think the conventional wisdom is that adding a temp probe through the side could create issues, though some others have used their spoons to make sure they clear the probe while pulling the bag. I'd be too worried about a snag to do that though.
I guess the real question is what do you want to accomplish by adding a thermometer to the side? If you just want to monitor temps, I like RM's suggestion of the hole in the lid with the long stemmed probe. Another option is using a waterproof electronic probe thermometer with a flexible lead. Personally, I just use a hand held electronic thermometer to check temps every 15 minutes when I open the pot to give the mash a stir. I have yet to have my mash lose so much temp (maybe 1-2 degrees in an hour) that I am worried I need to monitor it more closely.
Are you seeing bigger temp losses? If you are, you might ry insulating your kettle during the mash to keep your heat loss down. I use a large moving blanket which I can wrap around my pot and burner to keep heat in. It works, even in the cold.