On occasion I've accidentally left a capo on (overnight). Does this decrease the life of the strings, staying in tune time, hurt the neck, or anything else that's bad?
I would certainly not leave the capo on my fretboard when not in use. I cannot say it visibly hurts the neck for sure but it does wear out the strings. Here is a wonderful piece of advice from Lee Griffith in his article, A Capo is a Wonderful Thing:
One caution is important to mention. Do not leave the capo on the instrument when not playing it. The capo, when clamped on the neck, holds the strings down on the fretboard and creates extra tension on the neck and the top of the guitar. All acoustic guitars are destined, at some point in time, to have problems due to the tension of the strings. Why hasten the process by leaving a capo clamped on your guitar?
My question is, why do you want to leave the capo on the guitar all the time? To keep the guitar in a higher-than-normal pitch, or to lower the action?
A properly set-up guitar will have very low action without buzzing, equally as low as you'd get with a capo in place. It is also a lot more fun to play.
If you want higher than standard tuning, then take the guitar to your local guitar-repairshop and talk to the head tech. Tell him you want to keep your guitar in a higher tuning than normal but don't necessarily want to keep using a capo to achieve it. They can suggest lighter-guage string brands you can tune a bit higher, and then tweak the guitar so any increased string tension won't raise the action. The idea with the lighter gauge strings is to help reduce the tension at the higher pitch, but odds are good you'd have to have a minor tweak to keep the action feeling nice and comfortable.
The only times I'd use a capo is to get a particular sound, since stopping the strings at the 5th, 7th or 12th fret sounds very different than completely open strings. Or, because a particular song calls for it because that's how the original artist played it.
I personally would expect the most damage might actually be to the capo, because I would expect that prolonged contact with the strings might cause permanent grooves in the rubber or soft plastic pad of the capo, similar to what might happen if you were to hold a chord shape with your fingers for the same amount of time. I don't know about others, but my finger tips show signs of wear after playing four sets at the bar. I think a capo might also.