You tune your guitar, and as you start to play, certain strings seem to pop out of tuning. Especially when bending the strings!
This can be caused by your string catching in the nut. The tension is not always even between the head of the guitar and the rest of the string when this happens.
When changing your strings, take a #2 pencil (Graphite) and run it through each groove on the nut. (This is part the strings rest on where the head meets the neck.)
The presence of a little graphite in these grooves will help allow the tension to equalize properly so your whole string will be in tune properly when your tuner says it is.