When I changed my flat tire during the Waves to Wine ride, I was so slow that:
- You could have timed me using a sundial
- I had no less than 5 meaningful conversations with some of the locals
- The census bureau was going to add me as a resident of the town
I got off to a good start -- removed the wheel from the frame, got the tire off the wheel, found the source of the flat.
I lost a little time by not slightly inflating the new tube before mounting it.
The real time sink was that the tire didn't look like it was seated properly. I tried re-doing it a couple of times, but it just didn't look right. Perfectionism is a horrible thing! I finally decided that I wanted to finish the ride before sundown, so I did one more try at seating tube & tire, inflated the tire, put it back on, cleaned up my mess, and I was on my way.
Sometimes I think it'd be helpful if tubes were different colors than your tires. That way it'd be really, really simple to make sure that your tube wasn't stuck between the tire & the rim. But maybe that's just me.
I'll get back on the bike soon, I promise!