Haven't been through all the posts yet today, so forgive me if someone has already made some of these points.

A lot of people wonder why some way of inspecting the wing and replacing a tile was not used.

A primary reason this could not be done on Columbia is because the payload bay airlock door had a Spacehab module assembly bolted over it. As far as I know, there was no way to leave this particular Shuttle in space, even with a spacesuit, short of depressurizing the entire cabin and going out the main door, which I am not even sure is possible.

NASA looked into tile replacement in orbit, but research showed that the risks of such a maneuver outweighed the benefits. For one thing, someone told me, it was found that an astronaut buzzing around the tiles was likely to do additional damage to other tiles.

I wonder if it might be possible to invent a little remote-controlled widget capable of buzzing around the outside of the Shuttle with a little camera. Such a device could be kept in the payload bay, and be about the size of a soccer ball. Care would have to be taken by installing proximity sensors, maybe a padded exterior, or other precautions to make sure, again, that more damage could not be done by running the widget into undamaged tiles. This would not help repairs, but at least you would have the information. With sufficient thruster capability, such a gadget might also find use as a "life ring" to haul a wire out to a spacesuited astronaut who may have drifted away from the Shuttle or Space Station for some reason.

Experiments have been done with a small service robot that is designed to buzz around inside the Space Station acting as an assistant. I can't find the references because I don't remember what they called it, but it looked like a little red softball with gadgets on it. Very similar to the practice droid Luke Skywalker used for lightsaber practice.